MULTI-LEVEL FACTORIAL DESIGNS WITH MINIMUM NUMBERS OF LEVEL CHANGES

The order of experimental runs in a fractional factorial experiment is essential when the cost of level changes in factors is considered. The generalized foldover scheme given by [1] Coster, D. C. and Cheng, C. S. 1988. Minimum cost trend free run orders of fractional factorial designs. The Annals of Statistics, 16: 1188–1205. [Crossref], [Web of Science ®] , [Google Scholar]gives an optimal order to experimental runs in an experiment with specified defining contrasts. An experiment can be specified by a design requirement such as resolution or estimation of some interactions. To meet such a requirement, we can find several sets of defining contrasts. Applying the generalized foldover scheme to these sets of defining contrasts, we obtain designs with different numbers of level changes and then the design with minimum number of level changes. The difficulty is to find all the sets of defining contrasts. An alternative approach is investigated by [2] Cheng, C. S., Martin, R. J. and Tang, B. 1998. Two-level factorial designs with extreme numbers of level changes. The Annals of Statistics, 26: 1522–1539. [Crossref], [Web of Science ®] , [Google Scholar]for two-level fractional factorial experiments. In this paper, we investigate experiments with all factors in slevels.     

RAO'S STATISTIC FOR THE ANALYSIS OF UNIFORM ASSOCIATION IN CROSS-CLASSIFICATIONS

In this paper we introduce a new measure for the analysis of association in cross-classifications having ordered categories. Association is measured in terms of the odd-ratios in 2 × 2 subtables formed from adjacent rows and adjacent columns. We focus our attention in the uniform association model. Our measure is based in the family of divergences introduced by Burbea and Rao [1] Burbea, J. and Rao, C. R. 1982a. On the convexity of some divergence measures based on entropy functions. IEEE Transactions on Information Theory, 28: 489–495. [Crossref], [Web of Science ®] , [Google Scholar]. Some well-known sets of data are reanalyzed and a simulation study is presented to analyze the behavior of the new families of test statistics introduced in this paper.     

A MONTE CARLO COMPARISON OF VARIOUS ASYMPTOTIC APPROXIMATIONS TO THE DISTRIBUTION OF INSTRUMENTAL VARIABLES ESTIMATORS

ABSTRACT

We examine empirical relevance of three alternative asymptotic approximations to the distribution of instrumental variables estimators by Monte Carlo experiments. We find that conventional asymptotics provides a reasonable approximation to the actual distribution of instrumental variables estimators when the sample size is reasonably large. For most sample sizes, we find Bekker[11] Bekker, P. A. 1994. Alternative Approximations to the Distributions of Instrumental Variable Estimators. Econometrica, 62: 657–681. [Crossref], [Web of Science ®] , [Google Scholar] asymptotics provides reasonably good approximation even when the first stage R ² is very small. We conclude that reporting Bekker[11] Bekker, P. A. 1994. Alternative Approximations to the Distributions of Instrumental Variable Estimators. Econometrica, 62: 657–681. [Crossref], [Web of Science ®] , [Google Scholar] confidence interval would suffice for most microeconometric (cross-sectional) applications, and the comparative advantage of Staiger and Stock[5] Staiger, D. and Stock, J. H. 1997. Instrumental Variables Regression with Weak Instruments. Econometrica, 65: 556–586. [Crossref], [Web of Science ®] , [Google Scholar] asymptotic approximation is in applications with sample sizes typical in macroeconometric (time series) applications.     

COMBINING THE LIU ESTIMATOR AND THE PRINCIPAL COMPONENT REGRESSION ESTIMATOR

In this paper we introduce a class of estimators which includes the ordinary least squares (OLS), the principal components regression (PCR) and the Liu estimator [1] Liu, K. 1993. A new class of biased estimate in linear regression. Communications in Statistics – Theory and Methods, 22(2): 393–402. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]. In particular, we show that our new estimator is superior, in the scalar mean-squared error (mse) sense, to the Liu estimator, to the OLS estimator and to the PCR estimator.     

RANDOM PERMUTATION TESTING IN MULTIPLE LINEAR REGRESSION

We developed an alternative random permutation testing method for multiple linear regression, which is an improvement over the existing one proposed by [1] Kennedy, P. E. 1995. Randomization tests in econometrics. Journal of Business and Economic Statistics, 13: 85–94. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] or [2] Freedman, D. and Lane, D. 1983. A nonstochastic interpretation of reported significance levels. Journal of Business and Economic Statistics, 1: 292–298. [Taylor & Francis Online] , [Google Scholar].     

Two Statistics for Unconditional Exact Tests in Matched-Pairs Design

Abstract

In a recent article Hsueh et al. (Hsueh, H.-M., Liu, J.-P., Chen, J. J. (2001 Hsueh, H.-M., Liu, J.-P. and Chen, J. J. 2001. Unconditional exact tests for equivalence or noninferiority for paired binary endpoints. Biometrics, 57: 478–483. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Unconditional exact tests for equivalence or noninferiority for paired binary endpoints. Biometrics 57:478–483.) considered unconditional exact tests for paired binary endpoints. They suggested two statistics one of which is based on the restricted maximum-likelihood estimator. Properties of these statistics and the related tests are treated in this article.     

A NOTE ON ‘A COMPARISON OF BAYES AND MAXIMUM LIKELIHOOD ESTIMATION OF THE INTRACLASS CORRELATION COEFFICIENT’

Palmer and Broemeling [1] Palmer, J. L. and Broemeling, L. D. 1990. A Comparison of Bayes and Maximum Likelihood Estimation of the Intraclass Correlation Coefficient. Comm. Statist.-Theory Meth, 19: 953–975. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] compare Bayes and maximum likelihood estimates of the intraclass correlation (ICC). The prior information in their derivation of the Bayes estimator is placed on the variance components instead of the ICC itself. This paper finds a Bayes estimator of the ICC with the prior placed on the ICC. Bayes estimates based on three different priors are then compared to method of moments estimate.     

A NOTE ON ESTIMATING THE NUMBER OF SUPERIMPOSED EXPONENTIAL SIGNALS BY THE CROSS-VALIDATION APPROACH

In this paper, a procedure based on the delete-1 cross-validation is given for estimating the number of superimposed exponential signals, its limiting behavior is explored and it is shown that the probability of overestimating the true number of signals is greater than a positive constant for sufficiently large samples. Also a general procedure based on the cross-validation is presented when the deletion proceeds according to a collection of subsets of indices. The result is similar to the delete-1 cross-validation if the number of deletions is fixed. The simulation results are provided for the performance of the procedure when the collections of subsets of indices are chosen as those suggested by Shao [1] Shao, J. 1993. Linear model selection by cross-validation. J. Amer. Statist. Assoc., 88: 486–494. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]in a linear model selection problem.     

ESTIMATION OF PARAMETERS IN ARFIMA PROCESSES: A SIMULATION STUDY

It is known that, in the presence of short memory components, the estimation of the fractional parameter d in an Autoregressive Fractionally Integrated Moving Average, ARFIMA(p, d, q), process has some difficulties (see [1] Smith, J., Taylor, N. and Yadav, S. 1997. Comparing the bias and misspecification in ARFIMA models. Journal of Time Series Analysis, 18(5): 507–527. [Crossref] , [Google Scholar]). In this paper, we continue the efforts made by Smith et al. [1] Smith, J., Taylor, N. and Yadav, S. 1997. Comparing the bias and misspecification in ARFIMA models. Journal of Time Series Analysis, 18(5): 507–527. [Crossref] , [Google Scholar] and Beveridge and Oickle [2] Beveridge, S. and Oickle, C. 1993. Estimating fractionally integrated time series models. Economics Letters, 43: 137–142.  [Google Scholar] by conducting a simulation study to evaluate the convergence properties of the iterative estimation procedure suggested by Hosking [3] Hosking, J. 1981. Fractional differencing. Biometrika, 68(1): 165–176. [Crossref], [Web of Science ®] , [Google Scholar]. In this context we consider some semiparametric approaches and a parametric method proposed by Fox-Taqqu[4] Fox, R. and Taqqu, M. S. 1986. Large-sample properties of parameter estimates for strongly dependent stationary gaussian time series. The Annals of Statistics, 14(2): 517–532. [Crossref], [Web of Science ®] , [Google Scholar]. We also investigate the method proposed by Robinson [5] Robinson, P. M. 1995a. Log-periodogram regression of time series with long range dependence. The Annals of Statistics, 23(3): 1048–1072. [Crossref], [Web of Science ®] , [Google Scholar] and a modification using the smoothed periodogram function.     

POOLED SLICING METHODS VERSUS SLICING METHODS

We consider the semiparametric regression model introduced by [1] Duan, N. and Li, K. C. 1991. Slicing regression: a link-free regression method. The Annals of Statistics, 19: 505–530. [Crossref], [Web of Science ®] , [Google Scholar]. The dependent variable y is linked to the index x′ β through an unknown link function. [1] Duan, N. and Li, K. C. 1991. Slicing regression: a link-free regression method. The Annals of Statistics, 19: 505–530. [Crossref], [Web of Science ®] , [Google Scholar] and [2] Li, K. C. 1991. Sliced inverse regression for dimension reduction, with discussions. Journal of the American Statistical Association, 86: 316–342. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] present Slicing methods (the Sliced Inverse Regression methods SIR-I, SIR-II and SIR_α) in order to estimate the direction of the unknown slope parameter β. These methods are computationally simple and fast but depend on the choice of an arbitrary slicing fixed by the user. When the sample size is small, the number and the position of slices have an influence on the estimated direction. In this paper, we suggest to use the corresponding Pooled Slicing methods: PSIR-I (proposed by [3] Aragon, Y. and Saracco, J. 1997. Sliced Inverse Regression (SIR): an appraisal of small sample alternatives to slicing. Computational Statistics, 12: 109–130. [Web of Science ®] , [Google Scholar]), PSIR-II and PSIR_α. These methods combine the results from a number of slicings. We compare the sample behaviour of Slicing and Pooled Slicing methods on simulations. We also propose a practical choice of α in SIR_α and PSIR_α methods.     

MODIFICATION OF KELLY AND RICE METHOD FOR SYNERGISM TESTS

ABSTRACT

In this paper, we present a modified Kelly and Rice method for testing synergism. This approach is consistent with Berenbaum's1-3 Berenbaum, M.C. 1977. Synergism, Additivism, and Antagonism in Immuno-Suppression: A Critical Review. Clinical and Experimental Immunology, 28: 1–18. Berenbaum, M.C. 1985. The Expected Effect of a Combination of Agents: The General Solution. Journal of Theoretical Biology, 114: 413–431. Berenbaum, M.C. 1989. What is Synergism? Pharmacological Reviews. 41: 93–141.   framework for additivity. The delta method[4] Bishop, Y.M., Fienberg, S.E. and Holland, P.W. 1975. Discrete Multivariate Analysis: Theory and Practice Massachusetts: MIT Press.  [Google Scholar] is applied to obtain the estimated variance for the predicted additivity proportion. A Monte Carlo simulation study for the evaluation of the method's performance, i.e., global overall tests for synergism, is also discussed. Kelly and Rice[5] Kelly, C. and Rice, J. 1990. Monotone Smoothing with Application to Dose-Response Curves and the Assessment of Synergism. Biometrics, 46: 1071–1085. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] do not provide a correct test statistic because the variance is underestimated. Hence, the performance of the Kelly–Rice[5] Kelly, C. and Rice, J. 1990. Monotone Smoothing with Application to Dose-Response Curves and the Assessment of Synergism. Biometrics, 46: 1071–1085. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] method is generally anti-conservative, based on the simulation findings. In addition, the overall test of synergism with χ²(r) from the modified Kelly and Rice method for larger sample sizes is better than that with χ²(1) from the modified Kelly and Rice method.     

Group Variable Selection with Oracle Property by Weight-Fused Adaptive Elastic Net Model for Strongly Correlated Data

This paper is the generalization of weight-fused elastic net (Fu and Xu, 2012 Fu, G., Xu, Q. (2012). Grouping variable selection by weight fused elastic net for multi-collinear data. Communications in Statistics-Simulation and Computation 41(2):205–221.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), which performs group variable selection by combining weight-fused LASSO(wfLasso) and elastic net (Zou and Hastie, 2005 Zou, H., Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67(2):301–320.[Crossref], [Web of Science ®] , [Google Scholar]) penalties. In this study, the elastic net penalty is replaced by adaptive elastic net penalty (AdaEnet) (Zou and Zhang, 2009 Zou, H., Zhang, H. (2009). On the adaptive elastic-net with a diverging number of parameters. Annals of Statistics 37(4):1733–1751.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), and a new group variable selection algorithm with oracle property (Fan and Li, 2001 Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96(456):1348–1360.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Zou, 2006 Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101(476):1418–1429.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is obtained.     

Choosing Ridge Parameter for Regression Problems

ABSTRACT

Hoerl and Kennard (1970a Hoerl , A. E. , Kennard , R. W. ( 1970a ). Ridge regression: biased estimation for non-orthogonal problems . Tech. 12 : 55 – 67 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) introduced the ridge regression estimator as an alternative to the ordinary least squares estimator in the presence of multicollinearity. In this article, a new approach for choosing the ridge parameter (K), when multicollinearity among the columns of the design matrix exists, is suggested and evaluated by simulation techniques, in terms of mean squared errors (MSE). A number of factors that may affect the properties of these methods have been varied. The MSE from this approach has shown to be smaller than using Hoerl and Kennard (1970a Hoerl , A. E. , Kennard , R. W. ( 1970a ). Ridge regression: biased estimation for non-orthogonal problems . Tech. 12 : 55 – 67 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in almost all situations.     

Generalized linear regression models incorporating original outcome distributions

ABSTRACT

In this article, we propose an approach for incorporating continuous and discrete original outcome distributions into the usual exponential family regression models. The new approach is an extension of the works of Suissa (1991 Suissa, S. (1991). Binary methods for continuous outcomes: A parametric alternative. J. Clin. Epidemiol. 44:241–248.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Suissa and Blais (1995 Suissa, S., Blais, L. (1995). Binary regression with continuous outcomes. Stat. Med. 14:247–255.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), which present methods to estimate the risk of an event defined in a sample subspace of an original continuous outcome variable. Simulation studies are presented in order to illustrate the performance of the developed methodology. Real data sets are analyzed by using the proposed models.     

COMPUTING MARGINAL EFFECTS IN THE BOX–COX MODEL

ABSTRACT

This paper considers computation of fitted values and marginal effects in the Box–Cox regression model. Two methods, 1 the “smearing” technique suggested by Duan (see Ref. [10] Duan, N. 1983. Smearing Estimate: A Nonparametric Retransformation Method. J. Amer. Statistical Assoc., 78: 605–610. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and 2 direct numerical integration, are examined and compared with the “naive” method often used in econometrics.     

r-d Class Estimator Under Misspecification

Omission of some relevant explanatory variables and multicollinearity in regression models are very serious problems in applied works. There are some papers examining the multicollinearity and misspecification which is due to omission of some relevant explanatory variables, concurrently. To remedy the problem of multicollinearity, Kaç?ranlar and Sakall?o?lu (2001 Kaç?ranlar, S., Sakall?o?lu, S. (2001). Combining the Liu estimator and the principal component regression estimator. Commun. Stat. Theory Methods. 30:2699–2705.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) proposed the r-d class estimator that includes the ordinary least squares, principal components regression, and Liu estimators as special cases. The aim of this paper is to examine the performance of the r-d class estimator in misspecificied linear models.     

A Class of Improved Heteroskedasticity-Consistent Covariance Matrix Estimators

Abstract

The heteroskedasticity-consistent covariance matrix estimator proposed by White [White, H. A. (1980 White, H. A. 1980. Heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48: 817–838. [Crossref], [Web of Science ®] , [Google Scholar]). Heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48:817–838], also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto et al. [Cribari–Neto, F., Ferrari, S. L. P., Cordeiro, G. M. (2000 Cribari–Neto, F., Ferrari, S. L. P. and Cordeiro, G. M. 2000. Improved heteroscedasticity–consistent covariance matrix estimators. Biometrika, 87: 907–918. [Crossref], [Web of Science ®] , [Google Scholar]). Improved heteroscedasticity–consistent covariance matrix estimators. Biometrika 87:907–918] have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that are also commonly used by practitioners. These include the HC1, HC2, and HC3 estimators, which have proven to have superior small-sample behavior relative to White's estimator. This paper defines a general bias-correction mechamism that can be applied not only to White's estimator, but to variants of this estimator as well, such as HC1, HC2, and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.     

Tests Concerning Equicorrelation Matrices with Grouped Normal Data

ABSTRACT

This article considers three practical hypotheses involving the equicorrelation matrix for grouped normal data. We obtain statistics and computing formulae for common test procedures such as the score test and the likelihood ratio test. In addition, statistics and computing formulae are obtained for various small sample procedures as proposed in Skovgaard (2001 Skovgaard , I. M. . ( 2001 ). Likelihood asymptotics . Scand. J. Statist. . 28 : 3 – 32 . [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). The properties of the tests for each of the three hypotheses are compared using Monte Carlo simulations.     

THE SEQUENTIAL BOOTSTRAP: A COMPARISON WITH REGULAR BOOTSTRAP

Based on Bradley Efron's observation that individual resamples in the regular bootstrap have support on approximately 63% of the original observations, C. R. Rao, P. K. Pathak and V. I. Koltchinskii [1] Rao, C. R., Pathak, P. K. and Koltchinskii, V. I. 1997. Bootstrap by Sequential Resampling. Journal of Statistical Planning and Inference, 64: 257–281. [Crossref], [Web of Science ®] , [Google Scholar]have proposed a sequential resampling scheme. This sequential bootstrap stabilizes the information content of each resample by fixing the number of unique observations and letting N, the number of observatons in each resample, vary. The Rao-Pathak-Koltchinskii paper establishes the asymptotic correctness (consistency) of the sequential bootstrap. The main object of our investigation is to study the empirical properties of the Rao-Pathak-Koltchinskii sequential bootstrap as compared to the regular bootstrap. In all our settings, sequential bootstrap performs as well or better than regular bootstrap. In the particular case where we estimate standard errors of sample medians, we find that sequential bootstrap outperforms regular bootstrap by reducing variability in the final bootstrap estimates.     

REGRESSION DIAGNOSTIC USING LOCAL INFLUENCE: A REVIEW

The local influence approach of Cook [1] Cook, R. D. 1986. Assessment of Local Influence. Journal Of The Royal Statistical Society Series B-Methodological, 48: 133–169.  [Google Scholar]to regression diagnostic is developed and discussed, and compared with Cook's [2] Cook, R. D. 1977. Detection of Influential Observations in Linear Regression. Technometrics, 19: 15–18. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]deletion approach. The ability of the local influence approach to handle cases simultaneously, as well as some of its theoretical and practical difficulties, are reviewed. The perturbation ideas of the approach are applied to the linear model making distinction between the local perturbations on the assumptions of the model and the data.