Instrumental variable estimation of factor models with possibly many variables

In this paper, we consider the instrumental variables (IV) estimation of factor models. In the psychometrics literature, although the two-stage least squares (2SLS) estimator is routinely used in IV estimation of factor models, alternative estimators have been proposed in the econometrics literature. Therefore, in this paper, we compare the performance of these alternative IV estimators in the context of factor models. Monte Carlo simulation results reveal that the HLIM/HFUL estimator by Hausman et al. (2012 Hausman, J., W. K. Newey, T. Woutersen, J. C. Chao, and N. R. Swanson. 2012. Instrumental variable estimation with heteroskedasticity and many instruments. Quantitative Economics 3:211–55. [Google Scholar]) outperforms the 2SLS estimator and performs best in many cases.     

Vector error correction heterogeneous autoregressive forecast model of realized volatility and implied volatility

A vector error correction model is proposed for forecasting realized volatility which takes advantage of the cointegration relation between realized volatility and implied volatility. The model is constructed by adding a cointegration error term to a vector-and-unit-root version of the heterogeneous autoregressive (HAR) model of Corsi (2009 Corsi, F. 2009. A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics 7 (2):174–96. [Google Scholar]). The proposed model is easier to implement, extend, and interpret than fractional cointegration models. A Monte Carlo simulation and real data analysis reveal advantages of the proposed model over other existing models of Corsi (2009 Corsi, F. 2009. A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics 7 (2):174–96. [Google Scholar]), Busch Christensen and Nielsen (2011 Busch, T., B. J. Christensen, and M. Nielsen. 2011. The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets. Journal of Econometrics 160 (1):48–57. [Google Scholar]), Cho and Shin (2016 Cho, S. J. and D. W. Shin. 2016. An integrated heteroscedastic autoregressive model for forecasting long-memory volatilities. Journal of the Korean Statistical Society, 45:371–380. [Google Scholar]), and Bollerslev Patton, and Quaedvlieg (2016 Bollerslev, T., A. J. Patton, and R. Quaedvlieg. 2016. Exploiting the errors:A simple approach for improved volatility forecasting. Journal of Econometrics 192:1-18. [Google Scholar]).     

A cost-effective computational approach with non response on two occasions

Abstract

The present study is an attempt to equip a strategy with a cost-effective computational approach when non response is present under two occasion sampling. We have applied our computational cost strategy over Choudhary et al. (2004 Choudhary, R. K., H. V. L. Bathla, and U. C. Sud. 2004. On non-response in sampling on two occasions. Journal of the Indian Society of Agricultural Statistics 58(3):331–43. [Google Scholar])’s non response setup for fixed precision and evaluated cost. In addition, we have also computed variance for some fixed cost. We have discussed the aforementioned procedure for three cases as when there is non response present on both occasions, first occasion and second occasion. A numerical illustration is demonstrated for validation of improved cost methodology where we also work out with optimum unmatched or matched fraction while Choudhary et al. (2004 Choudhary, R. K., H. V. L. Bathla, and U. C. Sud. 2004. On non-response in sampling on two occasions. Journal of the Indian Society of Agricultural Statistics 58(3):331–43. [Google Scholar]) do not provide the direct optimal result.     

Bias corrected empirical Bayes confidence intervals for the selected mean

Empirical Bayes (EB) methods are very useful for post selection inference. Following Datta et al. (2002 Datta, G. S., M. Ghosh, D. D. Smith, and P. Lahiri. 2002. On an asymptotic theory of conditional and unconditional coverage probabilities of empirical Bayes confidence intervals. Scandinavian Journal of Statistics 29:139–52.[Crossref], [Web of Science ®] , [Google Scholar]), we construct EB confidence intervals for the selected population mean. The EB intervals are adjusted to achieve the target coverage probabilities asymptotically up to the second order. Both unconditional coverage probabilities of EB intervals and corresponding probabilities conditional on ancillary statistics are found.     

Testing economic “genetic pleiotropy” for Box-Cox linear model

Abstract

Genetic pleiotropy occurs when a single gene influences two or more seemingly unrelated phenotypic traits. It is significant to detect pleiotropy and understand its causes. However, most current statistical methods to discover pleiotropy mainly test the null hypothesis that none of the traits is associated with a variant, which departures from the null to test just one associated trait or k associated traits. Schaid et al. (2016 Schaid, D. J., X. Tong, B. Larrabee, R. B. Kennedy, G. A. Poland, and J. P. Sinnwell. 2016. Statistical methods for testing genetic pleiotropy. Genetics 204 (2):483–97. doi:10.1534/genetics.116.189308.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) first proposed a sequential testing framework to analyze pleiotropy based on a linear model and a multivariate normal distribution. In this paper, we analyze the Economic pleiotropy which occurs when an economic action or policy influences two or more economic phenomena. In this paper, we extend the linear model to Box-Cox transformation model and proposed a new decision method. It improves the efficiency of hypothesis test and controls the Type I error. We then apply the method using economic data to multivariate sectoral employments in response to governmental expenditures and provide a quantitative assessment and some insights of different impacts from economic policy.     

Use of scrambled response for estimating mean of the sensitivity variable

Abstract

In this article, we propose new efficient and more generalized difference-cum-exponential type estimator and generalized-difference-cum-generalized exponential type estimators for estimating the mean of sensitivity variable using the auxiliary information. We also discuss theoretically that proposed generalized estimators are more efficient than Sousa et al. (2010 Sousa, R., J. Shabbir, P. C. Real, and S. Gupta. 2010. Ratio estimation of the mean of a sensitive variable in the presence of auxiliary information. Journal of Statistical Theory and Practice 4 (3):495–507.[Taylor & Francis Online] , [Google Scholar]), Gupta et al. (2012 Gupta, S., J. Shabbir, R. Sousa, and P. C. Real. 2012. Estimation of the mean of a sensitive variable in the presence of auxiliary information. Communications in Statistics-Theory and Methods 41:1–12.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Koyuncu, Gupta, and Sousa (2014 Koyuncu, N., S. Gupta, and R. Sousa. 2014. Exponential-type estimators of the mean of a sensitive variable in the presence of non sensitive auxiliary information. Communications in Statistics-Simulation and Computation 43 (7):1583–94. doi: 10.1080/03610918.2012.737492.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) estimators. Results from a real life application and simulation study are presented to demonstrate the performance of the proposed mean estimators in relation to some of the existing mean estimators.     

Letter to the Editor

The aim of this letter to acknowledge of priority on calibration estimation. There are numerous studies on calibration estimation in literature. The studies on calibration estimation are reviewed and it is found out that an existing calibration estimator is reprocessed in the recent paper published by Nidhi et al. (2007 Nidhi, B. V. S. Sisodia, Subedar Singh, and Sanjay K. Singh. 2017. Calibration approach estimation of the mean in stratified sampling and stratified double sampling. Commun.Statist.Theor.Meth. 46 (10):4932–4942.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).     

Zero-Inflated NGINAR(1) process

In this paper, we develop a zero-inflated NGINAR(1) process as an alternative to the NGINAR(1) process (Risti?, Nasti?, and Bakouch 2009 Risti?, M. M., A. S. Nasti?, and H. S. Bakouch. 2009. A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. Journal of Statistical Planning and Inference 139:2218–26.[Crossref], [Web of Science ®] , [Google Scholar]) when the number of zeros in the data is larger than the expected number of zeros by the geometric process. The proposed process has zero-inflated geometric marginals and contains the NGINAR(1) process as a particular case. In addition, various properties of the new process are derived such as conditional distribution and autocorrelation structure. Yule-Walker, probability based Yule-Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Forecasting performances of the model are discussed. Application to a real data set shows the flexibility and potentiality of the new model.     

Estimation of nonseparable models with censored dependent variables and endogenous regressors

In this article we develop a nonparametric estimator for the local average response of a censored dependent variable to endogenous regressors in a nonseparable model where the unobservable error term is not restricted to be scalar and where the nonseparable function need not be monotone in the unobservables. We formalize the identification argument put forward in Altonji, Ichimura, and Otsu (2012 Altonji, J. G., Ichimura, H., Otsu, T. (2012). Estimating derivatives in nonseparable models with limited dependent variables. Econometrica 80:1701–1719.[Crossref], [Web of Science ®] , [Google Scholar]), construct a nonparametric estimator, characterize its asymptotic property, and conduct a Monte Carlo investigation to study its small sample properties. Identification is constructive and is achieved through a control function approach. We show that the estimator is consistent and asymptotically normally distributed. The Monte Carlo results are encouraging.     

Test for comparing complete expectations of life of two groups

Abstract

Complete expectation of life of an individual gives an intuitive and interesting perspective on the ageing process and is an important concept in the insurance sector for determination of premium. We propose a new test for testing equality of complete expectations of life of two groups/populations. Power of the new test is calculated through simulations and compared with the power of the tests given by Berger, Boos, and Guess (1988 Berger, R. L., D. D. Boos, and F. M. Guess. 1988. Tests and confidence sets for comparing two mean residual life functions. Biometrics 44 (1):103–15.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and Aly (1997 Aly, E. E. A. A. 1997. Nonparametric tests for comparing two mean residual life functions. Lifetime Data Analysis 3 (4):353–66.[Crossref], [PubMed] , [Google Scholar]). It is observed that the proposed test statistic is more powerful than the competing tests for the cases considered in this paper. A real life illustration is included.     

Nonparametric test for stratum effects in the cox model with interval-censored data

The testing of the stratum effects in the Cox model is an important and commonly asked question in medical research as well as in many other fields. In this paper, we will discuss the problem where one observes interval-censored failure time data and generalize the procedure given in Sun and Yang (2000 Sun, J., and I. Yang. 2000. Nonparametric test for stratum effects in the cox model. Lifetime Data Analysis 6:321–30.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) for right-censored data. The asymptotic distribution of the new test statistic is established and the simulation study conducted for the evaluation of the finite sample properties of the method suggests that the generalized procedure seems to work well for practical situations. An application is provided.     

Adaptive estimation for varying coefficient models with nonstationary covariates

In this paper, the adaptive estimation for varying coefficient models proposed by Chen, Wang, and Yao (2015 Chen, Y., Q. Wang, and W. Yao. 2015. Adaptive estimation for varying coefficient models. Journal of Multivariate Analysis 137:17–31.[Crossref], [Web of Science ®] , [Google Scholar]) is extended to allowing for nonstationary covariates. The asymptotic properties of the estimator are obtained, showing different convergence rates for the integrated covariates and stationary covariates. The nonparametric estimator of the functional coefficient with integrated covariates has a faster convergence rate than the estimator with stationary covariates, and its asymptotic distribution is mixed normal. Moreover, the adaptive estimation is more efficient than the least square estimation for non normal errors. A simulation study is conducted to illustrate our theoretical results.     

Bayesian process monitoring schemes for the two-parameter exponential distribution

In this paper a Bayesian procedure is applied to obtain control limits for the location and scale parameters, as well as for a one-sided upper tolerance limit in the case of the two-parameter exponential distribution. An advantage of the upper tolerance limit is that it monitors the location and scale parameter at the same time. By using Jeffreys’ non-informative prior, the predictive distributions of future maximum likelihood estimators of the location and scale parameters are derived analytically. The predictive distributions are used to determine the distribution of the “run-length” and expected “run-length”. A dataset given in Krishnamoorthy and Mathew (2009 Krishnamoorthy, K., and T. Mathew. 2009. Statistical Tolerance Regions: Theory, Applications and Computation. Wiley Series in Probability and Statistics.[Crossref] , [Google Scholar]) are used for illustrative purposes. The data are the mileages for some military personnel carriers that failed in service. The paper illustrates the flexibility and unique features of the Bayesian simulation method.     

Survival analysis for a new compounded bivariate failure time distribution in shock and competing risk models via an EM algorithm

Abstract

In this paper, two bivariate models based on the proposed methods of Marshall and Olkin are introduced. In the first model, the new bivariate distribution is presented based on the proposed method of Marshall and Olkin (1967 Marshall, A. W., and I. Olkin. 1967. A multivariate exponential distribution. Journal of the American Statistical Association 62 (317):30–44. doi: 10.2307/2282907.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) which has natural interpretations, and it can be applied in fatal shock models or in competing risks models. In the second model, the proposed method of Marshall and Olkin (1997 Marshall, A. W., and I. Olkin. 1997. A new method of adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika 84 (3):641–52. doi: 10.1093/biomet/84.3.641.[Crossref], [Web of Science ®] , [Google Scholar]) is generalized to bivariate case and a new bivariate distribution is introduced. We call these new distributions as the bivariate Gompertz (BGP) distribution and bivariate Gompertz-geometric (BGPG) distribution, respectively. Moreover, the BGP model can be obtained as a special case of the BGPG model. Then, we present various properties of the new bivariate models. In this regard, the joint and conditional density functions, the joint cumulative distribution function can be obtained in compact forms. Also, the aging properties and the bivariate hazard gradient are discussed. This model has five unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze three real data sets for illustrative purposes.     

A new stratified three-stage unrelated randomized response model for estimating a rare sensitive attribute based on the Poisson distribution

This article suggests an efficient method of estimating a rare sensitive attribute which is assumed following Poisson distribution by using three-stage unrelated randomized response model instead of the Land et al. model (2011 Land, M., S. Singh, and S. A. Sedory. 2011. Estimation of a rare sensitive attribute using poisson distribution. Statistics 46 (3):351–60. doi:10.1080/02331888.2010.524300.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) when the population consists of some different sized clusters and clusters selected by probability proportional to size(:pps) sampling. A rare sensitive parameter is estimated by using pps sampling and equal probability two-stage sampling when the parameter of a rare unrelated attribute is assumed to be known and unknown.

We extend this method to the case of stratified population by applying stratified pps sampling and stratified equal probability two-stage sampling. An empirical study is carried out to show the efficiency of the two proposed methods when the parameter of a rare unrelated attribute is assumed to be known and unknown.     

Complete convergence for weighted sums of negatively dependent random variables under the sub-linear expectations

In this article, we study complete convergence theorems for weighted sums of negatively dependent random variables under the sub-linear expectations. Our results extend the corresponding results of Sung (2012 Sung, S. H. 2012. A note on the Complete convergence for weighted sums of negatively dependent random variables. Journal of Inequalities and Applications 2012:158, 10 pages. [Google Scholar]) relative to the classical probability.     

Fitting competing risks data to bivariate Pareto models

This paper revisits two bivariate Pareto models for fitting competing risks data. The first model is the Frank copula model, and the second one is a bivariate Pareto model introduced by Sankaran and Nair (1993 Sankaran, P. G., and N. U. Nair. 1993. A bivariate Pareto model and its applications to reliability. Naval Research Logistics 40 (7):1013–1020. doi:10.1002/1520-6750(199312)40:7%3c1013::AID-NAV3220400711%3e3.0.CO;2-7.[Crossref], [Web of Science ®] , [Google Scholar]). We discuss the identifiability issues of these models and develop the maximum likelihood estimation procedures including their computational algorithms and model-diagnostic procedures. Simulations are conducted to examine the performance of the maximum likelihood estimation. Real data are analyzed for illustration.     

A nonparametric specification test for the volatility functions of diffusion processes

This paper develops a new test for the parametric volatility function of a diffusion model based on nonparametric estimation techniques. The proposed test imposes no restriction on the functional form of the drift function and has an asymptotically standard normal distribution under the null hypothesis of correct specification. It is consistent against any fixed alternatives and has nontrivial asymptotic power against a class of local alternatives with proper rates. Monte Carlo simulations show that the test performs well in finite samples and generally has better power performance than the nonparametric test of Li (2007 Li, F. (2007). Testing the parametric specification of the diffusion function in a diffusion process. Econometric Theory 23(2):221–250.[Crossref], [Web of Science ®] , [Google Scholar]) and the stochastic process-based tests of Dette and Podolskij (2008 Dette, H., Podolskij, M. (2008). Testing the parametric form of the volatility in continuous time diffusion models–a stochastic process approach. Journal of Econometrics 143(1):56–73.[Crossref], [Web of Science ®] , [Google Scholar]). When applying the test to high frequency data of EUR/USD exchange rate, the empirical results show that the commonly used volatility functions fit more poorly when the data frequency becomes higher, and the general volatility functions fit relatively better than the constant volatility function.     

A shift-dependent generalized cumulative entropy of order n

Recently, a shift-independent information measure known as generalized cumulative entropy of order n (GCE_n) was proposed by Kayal (2016 Kayal, S. 2016. On generalized cumulative entropies. Probability in Engineering and Informational Sciences 30:640–62. [Google Scholar]). In this communication, we propose a shift-dependent version of GCE_n. Various properties including the effect of transformations, bounds etc. have been discussed. Several relationships of the shift-dependent GCE_n with some well-known reliability measures are studied. Few characterization results are obtained. We derive an estimator for the proposed measure via empirical distribution function approach. Large sample properties of the estimator are studied when independent observations are taken from a Weibull distribution.