Copula structure analysis

Summary.  We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical results we observe in a simulation study the performance of the estimators: the theoretical asymptotic behaviour of the statistics can be observed even for small sample sizes. Finally, we show our method at work for a financial data set and explain differences between our copula-based approach and the classical approach. Our new method yielear models also.     

Shrinkage inverse regression estimation for model-free variable selection

Summary.  The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root n estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis.     

Improved likelihood inferences for Weibull regression model

A general procedure is developed for bias-correcting the maximum likelihood estimators (MLEs) of the parameters of Weibull regression model with either complete or right-censored data. Following the bias correction, variance corrections and hence improved t-ratios for model parameters are presented. Potentially improved t-ratios for other reliability-related quantities are also discussed. Simulation results show that the proposed method is effective in correcting the bias of the MLEs, and the resulted t-ratios generally improve over the regular t-ratios.     

Generalized correlation and kernel causality with applications in development economics

New generalized correlation measures of 2012, GMC(Y|X), use Kernel regressions to overcome the linearity of Pearson's correlation coefficients. A new matrix of generalized correlation coefficients is such that when |r*_ij| > |r*_ji|, it is more likely that the column variable X_j is what Granger called the “instantaneous cause” or what we call “kernel cause” of the row variable X_i. New partial correlations ameliorate confounding. Various examples and simulations support robustness of new causality. We include bootstrap inference, robustness checks based on the dependence between regressor and error, and on the out-of-sample forecasts. Data for 198 countries on nine development variables support growth policy over redistribution and Deaton's criticism of foreign aid. Potential applications include Big Data, since our R code is available in the online supplementary material.     

Notes on testing carry-over effects in continuous data under an incomplete block crossover design

We consider hypothesis testing and estimation of carry-over effects in continuous data under an incomplete block crossover design when comparing two experimental treatments with a placebo. We develop procedures for testing differential carry-over effects based on the weighted-least-squares (WLS) method. We apply Monte Carlo simulations to evaluate the performance of these test procedures in a variety of situations. We use the data regarding the forced expiratory volume in one second (FEV₁) readings taken from a double-blind crossover trial comparing two different doses of formoterol with a placebo to illustrate the use of test procedures proposed here.     

Estimation of variance in bivariate normal distribution after the preliminary test of homogeneity

A preliminary test estimator of variance in the bivariate normal distribution is proposed after the Pitman–Morgan test of homogeneity of two variances. The bias and mean square error of the estimator are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max–min criterion.     

Vine copula constructions of higher-dimensional dependent reliability systems

Copulas have proved to be very successful tools for the flexible modeling of dependence. Bivariate copulas have been deeply researched in recent years, while building higher-dimensional copulas is still recognized to be a difficult task. In this paper, we study the higher-dimensional dependent reliability systems using a type of decomposition called “vine,” by which a multivariate distribution can be decomposed into a cascade of bivariate copulas. Some equations of system reliability for parallel, series, and k-out-of-n systems are obtained and then decomposed based on C-vine and D-vine copulas. Finally, a shutdown system is considered to illustrate the results obtained in the paper.     

Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables

We propose an improved difference-cum-exponential ratio type estimator for estimating the finite population mean in simple and stratified random sampling using two auxiliary variables. We obtain properties of the estimators up to first order of approximation. The proposed class of estimators is found to be more efficient than the usual sample mean estimator, ratio estimator, exponential ratio type estimator, usual two difference type estimators, Rao (1991) estimator, Gupta and Shabbir (2008) estimator, and Grover and Kaur (2011) estimator. We use six real data sets in simple random sampling and two in stratified sampling for numerical comparisons.     

A fresh approach for intercession of nonresponse in multivariate longitudinal designs

The occurrence of nonresponse is very much plebeian in surveys, which troubles the analysis, and hence, an inappropriate inference is left out. To counterbalance the sour effects of the incompleteness, fresh imputation techniques have been proposed with the aid of multi-auxiliary variates for the estimation of population mean on successive waves. Properties of the proposed estimators have been elaborated, and they have been compared with the work of Priyanka et al. (2015). Detailed simulation study is carried out to substantiate the empirical and theoretical results. Several possible cases have been addressed in which nonresponse can occur.