Estimators for the Population Mean in the Case of Missing Data

We propose a class of estimators for the population mean when there are missing data in the data set. Obtaining the mean square error equations of the proposed estimators, we show the conditions where the proposed estimators are more efficient than the sample mean, ratio-type estimators, and the estimators in Singh and Horn (2000 Singh , S. , Horn , S. ( 2000 ). Compromised imputation in survey sampling . Metrika 51 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) and Singh and Deo (2003 Singh , S. , Deo , B. (2003). Imputation by power transformation. Statist. Pap. 44:555–579.[Crossref], [Web of Science ®] , [Google Scholar]) in the case of missing data. These conditions are also supported by a numerical example.     

Bayesian Robustness of the Positive False Discovery Rate

The positive false discovery rate was introduced by Storey (2003 Storey , J. D. (2003). The positive false discovery rate: a Bayesian interpretation and the q-value. Ann. Statist. 31:2013–2035.[Crossref], [Web of Science ®] , [Google Scholar]) as an alternative to the family wise error rate for the case in which we are simultaneously testing a large amount of hypotheses. The positive false discovery rate has a very nice Bayesian interpretation (as it was shown by Storey, 2003 Storey , J. D. (2003). The positive false discovery rate: a Bayesian interpretation and the q-value. Ann. Statist. 31:2013–2035.[Crossref], [Web of Science ®] , [Google Scholar]) and its robustness is analyzed. The emphasis is on the ε-contamination class (one of the most used classes of priors for Bayesian robustness) and it is shown that robustness is not obtained when the basic prior concentrates the probability on the null hypothesis.     

Bayesian Capture-Recapture Analysis: An Application in Modeling Semelparity of a Neotropical Didelphid Marsupial

We develop a series of Bayesian statistical models for estimating survival of a neotropic didelphid marsupial, the Brazilian gracile mouse opossum (Gracilinanus microtarsus). These models are based on the Cormack–Jolly–Seber model (Cormack, 1964 Cormack , R. M. ( 1964 ). Estimates of survival from the sighting of marked animals . Biometrika 51 : 429 – 438 .[Crossref], [Web of Science ®] , [Google Scholar]; Jolly 1965 Jolly , G. M. ( 1965 ). Explicit estimates from capture-recapture data with both death and immigration stochastic model . Biometrika 52 : 225 – 247 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Seber 1965 Seber , G. A. F. ( 1965 ). A note on the multiple recapture census . Biometrika 52 : 249 – 259 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) with both survival and recapture rates expressed as a function of covariates using a logit link. The proposed models allow taking into account heterogeneity in capture probability caused by the existence of different groups of individuals in the population. The models were applied to two cohorts (Cohort, 2000, 2001) with the first one including 14 and the second one 15 sampling occasions. The best models for each of the cohorts indicate that G. microtarsus is best described as partially semelparous, a condition in which mortality after the first mating is high but graded over time, with a fraction of males surviving for a second breeding season (Boonstra, 2005 Boonstra , R. ( 2005 ). Equipped for life: the adaptive role of the stress axis in male mammals . Journal of Mammalogy 86 : 236 – 247 .[Crossref], [Web of Science ®] , [Google Scholar]).     

The Identification of Potential Longitudinal Biomarkers and Measurements of Effectiveness for Biomarkers as Surrogates in Multivariate Survival Data

A proposed method based on frailty models is used to identify longitudinal biomarkers or surrogates for a multivariate survival. This method is an extention of earlier models by Wulfsohn and Tsiatis (1997 Wulfsohn , M. S. , Tsiatis , A. A. ( 1997 ). A joint model for survival and longitudinal data measured with error . Biometrics 53 ( 1 ): 330 – 339 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Song et al. (2002 Song , X. , Davidian , M. , Tsiatis , A. A. ( 2002 ). A Semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data . Biometrics 58 ( 4 ): 742 – 753 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). In this article, similar to Henderson et al. (2002 Henderson , R. , Diggle , P. J. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), a joint likelihood function combines the likelihood functions of the longitudinal biomarkers and the multivariate survival times. We use simulations to explore how the number of individuals, the number of time points per individual and the functional form of the random effects from the longitudianl biomarkers influence the power to detect the association of a longitudinal biomarker and the multivariate survival time. The proposed method is illustrate by using the gastric cancer data.     

Hazards Regression for Cancer Studies

The complication in analyzing tumor data is that the tumors detected in a screening program tend to be slowly progressive tumors, which is the so-called length-biased sampling that is inherent in screening studies. Under the assumption that all subjects have the same tumor growth function, Ghosh (2008 Ghosh , D. ( 2008 ). Proportional hazards regression for cancer studies . Biometrics 64 : 141 – 148 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) developed estimation procedures for proportional hazards model. In this article, by modeling growth function as a function of covariates, we demonstrate that Ghosh (2008 Ghosh , D. ( 2008 ). Proportional hazards regression for cancer studies . Biometrics 64 : 141 – 148 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar])'s approach can be extended to the case when each subject has a specific growth function. A simulation study is conducted to demonstrate the potential usefulness of the proposed estimators for the regression parameters in the proportional and additive hazards model.     

Nonparametric Knn estimation with monotone constraints

ABSTRACT

The K-nearest-neighbor (Knn) method is known to be more suitable in fitting nonparametrically specified curves than the kernel method (with a globally fixed smoothing parameter) when data sets are highly unevenly distributed. In this paper, we propose to estimate a nonparametric regression function subject to a monotonicity restriction using the Knn method. We also propose using a new convergence criterion to measure the closeness between an unconstrained and the (monotone) constrained Knn-estimated curves. This method is an alternative to the monotone kernel methods proposed by Hall and Huang (2001 Hall, P., Huang, L.-S. (2001). Nonparametric kernel regression subject to monotonicity constraints. The Annals of Statistics 29:624–647.[Crossref], [Web of Science ®] , [Google Scholar]), and Du et al. (2013 Du, P., Parmeter, C. F., Racine, J. S. (2013). Nonparametric kernel regression with multiple predictors and multiple shape constraints. Statistic Sinica 23:1347–1371.[Web of Science ®] , [Google Scholar]). We use a bootstrap procedure for testing the validity of the monotone restriction. We apply our method to the “Job Market Matching” data taken from Gan and Li (2016 Gan, L., Li, Q. (2016). Efficiency of thin and thick market. Journal of Econometrics 192(1):40–54.[Crossref], [Web of Science ®] , [Google Scholar]) and find that the unconstrained/constrained Knn estimators work better than kernel estimators for this type of highly unevenly distributed data.     

Modeling of Inverse Gaussian Frailty Model for Bivariate Survival Data

Shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor (frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this article, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions namely, Weibull, generalized exponential, and exponential power distribution. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. To estimate the parameters involved in these models we adopt Markov Chain Monte Carlo (MCMC) approach. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply these three models to a real life bivariate survival data set of McGilchrist and Aisbett (1991 McGilchrist , C. A. , Aisbett , C. W. ( 1991 ). Regression with frailty in survival analysis . Biometrics 47 : 461 – 466 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to kidney infection and a better model is suggested for the data.     

On Testing Sample Selection Bias Under the Multicollinearity Problem

ABSTRACT

This paper reviews and extends the literature on the finite sample behavior of tests for sample selection bias. Monte Carlo results show that, when the “multicollinearity problem” identified by Nawata (1993 Nawata , K. ( 1993 ). A note on the estimation of models with sample-selection biases . Economics Letters 42 : 15 – 24 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) is severe, (i) the t-test based on the Heckman–Greene variance estimator can be unreliable, (ii) the Likelihood Ratio test remains powerful, and (iii) nonnormality can be interpreted as severe sample selection bias by Maximum Likelihood methods, leading to negative Wald statistics. We also confirm previous findings (Leung and Yu, 1996 Leung , S. F. , Yu , S. ( 1996 ). On the choice between sample selection and two-part models . Journal of Econometrics 72 : 197 – 229 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]) that the standard regression-based t-test (Heckman, 1979 Heckman , J. J. ( 1979 ). Sample selection bias as a specification error . Econometrica 47 : 153 – 161 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]) and the asymptotically efficient Lagrange Multiplier test (Melino, 1982 Melino , A. ( 1982 ). Testing for sample selection bias . Review of Economic Studies 49 : 151 – 153 . [CSA] [Crossref], [Web of Science ®] , [Google Scholar]), are robust to nonnormality but have very little power.     

The Alpha-power Tobit Model

The main object of this article is to propose an extension of the tobit model for which the error distribution follows the power-normal distribution (Gupta and Gupta, 2008 Gupta , D. , Gupta , R. C. ( 2008 ). Analyzing skewed data by power normal model . Test 17 : 197 – 210 .[Crossref], [Web of Science ®] , [Google Scholar]). Inference is dealt with by using the likelihood approach. Simulation studies and application to a real data set are used to demonstrate the usefulness of the extension.     

Regression M-estimators with One Modified Form of Doubly Censored Data

In this article, we consider the M-estimators for the linear regression model when both response and covariate variables are subject to double censoring. The proposed estimators are constructed as some functional of three types of estimators for a bivariate survival distribution. The first two estimators are the generalizations of the Campbell and Földes (1982 Campbell, G. and Földes, A. 1982. “Large sample properties of nonparametric statistical inference”. In Nonparametric Statistical Inference., Edited by: Gnredenko, B. V., Puri, M. L. and Vineze, I. 103–122. Amsterdam: North-Holland.  [Google Scholar]) and Dabrowska (1988 Dabrowska, D. M. 1988. Kaplan-Meier estimate on the plane. Annals of Statistics, 18: 1475–1489. [Crossref], [Web of Science ®] , [Google Scholar]) estimators proposed by Shen (2009 Shen, P. S. 2009. Nonparametric estimation of the bivariate survival function one modified form of doubly censored data. Computational Statistics, 25: 203–313. [Crossref], [Web of Science ®] , [Google Scholar]). The third estimator is the generalization of the Prentice and Cai (1992 Prentice, R. L. and Cai, J. 1992. Covariance and survivor function estimation using censored multivariate failure time data. Biometrika, 79: 495–512. [Crossref], [Web of Science ®] , [Google Scholar]) estimator. The consistency of the proposed M-estimators is established. A simulation study is conducted to investigate the performance of the proposed estimators. Furthermore, the simple bootstrap methods are used to estimate standard deviations and construct interval estimators.     

A Broad Class of Partially Specified Autoregressions on Multi-Casting Data

Extending the bifurcating autoregressive (BAR) process (cf. Cowan and Staudte, 1986 Cowan , R. , Staudte , R. G. ( 1986 ). The bifurcating autoregression model in cell lineage studies . Biometrics 42 : 769 – 783 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) to multi-casting (multi-splitting) data, Hwang and Choi (2009 Hwang , S. Y. , Choi , M. S. ( 2009 ). Modeling and large sample estimation for multi-casting autoregression . Statist. Prob. Lett. 79 : 1943 – 1950 .[Crossref], [Web of Science ®] , [Google Scholar]) introduced multi-casting autoregression (MCAR, for short) defined on multi-casting tree structured data. This article is concerned with the case when the MCAR model is partially specified only through conditional mean and variance without directly imposing autoregressive (AR) structure. The resulting class of models will be referred to as P-MCAR (partially specified MCAR). The P-MCAR considerably enlarges the class of multi-casting models including (as special cases) MCAR, random coefficient MCAR, conditionally heteroscedastic multi-casting models and binomial-thinning processes. Moment structures for this broad P-MCAR class are investigated. Least squares (LS) estimation method is discussed and asymptotic relative efficiency (ARE) of the generalized-LS over ordinary-LS is obtained in a closed form. A simulation study is conducted to illustrate results.     

Relative Errors of Difference-Based Variance Estimators in Nonparametric Regression

Difference-based estimators for the error variance are popular since they do not require the estimation of the mean function. Unlike most existing difference-based estimators, new estimators proposed by Müller et al. (2003 Müller , U. , Schick , A. , Wefelmeyer , W. ( 2003 ). Estimating the error variance in nonparametric regression by a covariate-matched U-statistic . Statistics 37 : 179 – 188 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Tong and Wang (2005 Tong , T. , Wang , Y. ( 2005 ). Estimating residual variance in nonparametric regression using least squares . Biometrika 92 : 821 – 830 .[Crossref], [Web of Science ®] , [Google Scholar]) achieved the asymptotic optimal rate as residual-based estimators. In this article, we study the relative errors of these difference-based estimators which lead to better understanding of the differences between them and residual-based estimators. To compute the relative error of the covariate-matched U-statistic estimator proposed by Müller et al. (2003 Müller , U. , Schick , A. , Wefelmeyer , W. ( 2003 ). Estimating the error variance in nonparametric regression by a covariate-matched U-statistic . Statistics 37 : 179 – 188 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), we develop a modified version by using simpler weights. We further investigate its asymptotic property for both equidistant and random designs and show that our modified estimator is asymptotically efficient.     

A Nonparametric Test for Symmetry Based on Freeman and Halton's Ideas on Contingency Tables

In this article, we propose a nonparametric method to test for symmetry in bivariate data. By using the extension of Fisher's exact treatment for 2 × 2 contingency tables proposed by Freeman and Halton (1951 Freeman , G. H. , Halton , J. H. ( 1951 ). Note on an exact treatment of contingency tables, goodness of fit and other problems of significance . Biometrika 38 : 141 – 149 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), we can test the hypothesis of equal distribution for two samples of integer valued variables. Then, by counting the number of observations belonging to each cell of a symmetric, appropriately built grid, we can produce the two samples of integers required to use this test for equal distribution. The resulting test for symmetry is potentially extendible to higher dimensions. A simulation study is performed to compare with some known tests (Bowker, 1948 Bowker , A. H. ( 1948 ). A test for symmetry in contingency tables . Journal of the American Statistical Association 43 : 572 – 574 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Hollander, 1971 Hollander , M. ( 1971 ). A nonparametric test for bivariate symmetry . Biometrika 58-1 : 203 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]; and its improvement given in Krampe and Kuhnt, 2007 Krampe , A. , Kuhnt , S. ( 2007 ). Bowker's test for symmetry and modifications within the algebraic framework . Computational Statistics and Data Analysis 51 : 4124 – 4142 .[Crossref], [Web of Science ®] , [Google Scholar]). Our proposal represents a competitive option as a test for symmetry.     

A Comparison of Procedures for Controlling the False Discovery Rate in the Presence of Small Variance Genes: A Simulation Study

The Significance Analysis of Microarrays (SAM; Tusher et al., 2001 Tusher , V. G. , Tibshirani , R. , Chu , G. ( 2001 ). Significance analysis of microarrys applied to the ionizing radiation response . Proceedings of the National Academy of Sciences 98 : 5116 – 5121 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) method is widely used in analyzing gene expression data while controlling the FDR by using resampling-based procedure in the microarray setting. One of the main components of the SAM procedure is the adjustment of the test statistic. The introduction of the fudge factor to the test statistic aims at deflating the large value of test statistics due to the small standard error of gene-expression. Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) pointed out that the fudge factor does not effectively improve the power and the control of the FDR as compared to the SAM procedure without the fudge factor in the presence of small variance genes. Motivated by the simulation results presented in Lin et al. (2008 Lin , D. , Shkedy , Z. , Burzykowski , T. , Göhlmann , H. W. H. , De Bondt , A. , Perera , T. , Geerts , T. , Bijnens , L. ( 2008 ). Significance analysis of microarray (SAM) for comparisons of several treatments with one control . Biometric Journal, MCP 50 ( 5 ): 801 – 823 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), in this article, we extend our study to compare several methods for choosing the fudge factor in the modified t-type test statistics and use simulation studies to investigate the power and the control of the FDR of the considered methods.     

A Bayes Factor for Replications of ANOVA Results

ABSTRACT

With an increasing number of replication studies performed in psychological science, the question of how to evaluate the outcome of a replication attempt deserves careful consideration. Bayesian approaches allow to incorporate uncertainty and prior information into the analysis of the replication attempt by their design. The Replication Bayes factor, introduced by Verhagen and Wagenmakers (2014 Verhagen, J., and Wagenmakers, E.-J. (2014), “Bayesian Tests to Quantify the Result of a Replication Attempt,” Journal of Experimental Psychology: General, 143, 1457–1475. DOI: 10.1037/a0036731.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), provides quantitative, relative evidence in favor or against a successful replication. In previous work by Verhagen and Wagenmakers (2014 Verhagen, J., and Wagenmakers, E.-J. (2014), “Bayesian Tests to Quantify the Result of a Replication Attempt,” Journal of Experimental Psychology: General, 143, 1457–1475. DOI: 10.1037/a0036731.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), it was limited to the case of t-tests. In this article, the Replication Bayes factor is extended to F-tests in multigroup, fixed-effect ANOVA designs. Simulations and examples are presented to facilitate the understanding and to demonstrate the usefulness of this approach. Finally, the Replication Bayes factor is compared to other Bayesian and frequentist approaches and discussed in the context of replication attempts. R code to calculate Replication Bayes factors and to reproduce the examples in the article is available at https://osf.io/jv39h/.     

An Inverse-Probability-Weighted Approach to the Estimation of Successive Duration Times under Left-Truncation and Right-Censoring

In incident cohort studies, survival data often include subjects who have had an initiate event at recruitment and may potentially experience two successive events (first and second) during the follow-up period. Since the second duration process becomes observable only if the first event has occurred, left-truncation and dependent censoring arise if the two duration times are correlated. To confront the two potential sampling biases, Chang and Tzeng (2006 Chang , S.-H. , Tzeng , S.-J. (2006). Noparametric estimation of sojourn time distributions for truncated serial event data- a weight-adjusted approach. Lifetime Data Anal. 53–67.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) provided an inverse-probability-weighted (IPW) approach for estimating the joint probability function of successive duration times. In this note, an alternative IPW approach is proposed. A simulation study is conducted to compare the two IPW approaches.     

Using Frailty Models to Identify the Longitudinal Biomarkers in Survival Analysis

We introduce a score test to identify longitudinal biomarkers or surrogates for a time to event outcome. This method is an extension of Henderson et al. (2000 Henderson , R. , Diggle , P. , Dobson , A. ( 2000 ). Joint modelling of longitudinal measurements and event time data . Biostatistics 1 ( 4 ): 465 – 480 .[Crossref], [PubMed] , [Google Scholar], 2002 Henderson , R. , Diggle , P. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). In this article, a score test is based on a joint likelihood function which combines the likelihood functions of the longitudinal biomarkers and the survival times. Henderson et al. (2000 Henderson , R. , Diggle , P. , Dobson , A. ( 2000 ). Joint modelling of longitudinal measurements and event time data . Biostatistics 1 ( 4 ): 465 – 480 .[Crossref], [PubMed] , [Google Scholar], 2002 Henderson , R. , Diggle , P. , Dobson , A. ( 2002 ). Identification and efficacy of longitudinal markers for survival . Biostatistics 3 ( 1 ): 33 – 50 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) assumed that the same random effect exists in the longitudinal component and in the Cox model and then they can derive a score test to determine if a longitudinal biomarker is associated with time to an event. We extend this work and our score test is based on a joint likelihood function which allows other random effects to be present in the survival function.

Considering heterogeneous baseline hazards in individuals, we use simulations to explore how the factors can influence the power of a score test to detect the association of a longitudinal biomarker and the survival time. These factors include the functional form of the random effects from the longitudinal biomarkers, in the different number of individuals, and time points per individual. We illustrate our method using a prothrombin index as a predictor of survival in liver cirrhosis patients.     

Projection Pursuit Through Relative Entropy Minimization

Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, “Projection Pursuit”, Huber (1985 Huber , P. ( 1985 ). Projection pursuit . The Annals of Statistics 13 ( 2 ): 435 – 525 With discussion .[Crossref], [Web of Science ®] , [Google Scholar]) evidenced the interest of the Projection Pursuit method thanks to the factorization of a density into a Gaussian component and some residual density in a context of Kullback–Leibler divergence maximisation.

In the present article, we introduce a new algorithm, and in particular, a test for the factorisation of a density estimated from an iid sample.     

Generalized Scrambling in Quantitative Optional Randomized Response Models

Huang (2010 Huang , K. C. ( 2010 ). Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling . Metrika 71 : 341 – 352 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed an optional randomized response model using a linear combination scrambling which is a generalization of the multiplicative scrambling of Eichhorn and Hayre (1983 Eichhorn , B. H. , Hayre , L. S. ( 1983 ). Scrambled randomized response methods for obtaining sensitive quantitative data . J. Statist. Plann. Infer. 7 : 307 – 316 .[Crossref], [Web of Science ®] , [Google Scholar]) and the additive scrambling of Gupta et al. (2006, 2010). In this article, we discuss two main issues. (1) Can the Huang (2010 Huang , K. C. ( 2010 ). Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling . Metrika 71 : 341 – 352 .[Crossref], [Web of Science ®] , [Google Scholar]) model be improved further by using a two-stage approach?; (2) Does the linear combination scrambling provide any benefit over the additive scrambling of Gupta et al. (2010 Gupta , S. N. , Shabbir , J. , Sehra , S. ( 2010 ). Mean and sensitivity estimation in optional randomized response models . J. Statist. Plann. Infer. 140 : 2870 – 2874 .[Crossref], [Web of Science ®] , [Google Scholar])? We will note that the answer to the first question is “yes” but the answer to the second question is “no.”     

The Performance of Panel Cointegration Methods: Results from a Large Scale Simulation Study

This article presents results concerning the performance of both single equation and system panel cointegration tests and estimators. The study considers the tests developed in Pedroni (1999 Pedroni , P. ( 1999 ). Critical values for cointegration tests in heterogeneous panels with multiple regressors . Oxford Bulletin of Economics and Statistics 61 : 653 – 670 .[Crossref], [Web of Science ®] , [Google Scholar], 2004 Pedroni , P. ( 2004 ). Panel cointegration. Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis . Econometric Theory 20 : 597 – 625 .[Crossref], [Web of Science ®] , [Google Scholar]), Westerlund (2005 Westerlund , J. ( 2005 ). New simple tests for panel cointegration . Econometric Reviews 24 : 297 – 316 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Larsson et al. (2001 Larsson , R. , Lyhagen , J. , Löthgren , M. ( 2001 ). Likelihood-based cointegration tests in heterogeneous panels . Econometrics Journal 4 : 109 – 142 .[Crossref] , [Google Scholar]), and Breitung (2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and the estimators developed in Phillips and Moon (1999 Phillips , P. C. B. , Moon , H. R. ( 1999 ). Linear regression limit theory for nonstationary panel data . Econometrica 67 : 1057 – 1111 .[Crossref], [Web of Science ®] , [Google Scholar]), Pedroni (2000 Pedroni , P. ( 2000 ). Fully modified OLS for heterogeneous cointegrated panels . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 93 – 130 .[Crossref] , [Google Scholar]), Kao and Chiang (2000 Kao , C. , Chiang , M.-H. ( 2000 ). On the estimation and inference of a cointegrated regression in panel data . In: Baltagi , B. H. , ed. Nonstationary Panels, Panel Cointegration, and Dynamic Panels . Amsterdam : Elsevier , pp. 179 – 222 .[Crossref] , [Google Scholar]), Mark and Sul (2003 Mark , N. C. , Sul , D. ( 2003 ). Cointegration vector estimation by panel dynamic OLS and long-run money demand . Oxford Bulletin of Economics and Statistics 65 : 655 – 680 .[Crossref], [Web of Science ®] , [Google Scholar]), Pedroni (2001 Pedroni , P. ( 2001 ). Purchasing power parity tests in cointegrated panels . Review of Economics and Statistics 83 : 1371 – 1375 . [Google Scholar]), and Breitung (2005 Breitung , J. ( 2005 ). A parametric approach to the estimation of cointegration vectors in panel data . Econometric Reviews 24 : 151 – 173 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We study the impact of stable autoregressive roots approaching the unit circle, of I(2) components, of short-run cross-sectional correlation and of cross-unit cointegration on the performance of the tests and estimators. The data are simulated from three-dimensional individual specific VAR systems with cointegrating ranks varying from zero to two for fourteen different panel dimensions. The usual specifications of deterministic components are considered.