Bayesian meta-analysis of correlation coefficients through power prior

This article proposes a Bayesian approach for meta-analysis of correlation coefficients through power prior. The primary purpose of this method is to allow meta-analytic researchers to evaluate the contribution and influence of each individual study to the estimated overall effect size though power prior. We use the relationship between high-performance work systems and financial performance as an example to illustrate how to apply this method. We also introduce free online software that can be used to conduct Bayesian meta-analysis proposed in this study. Implications and future directions are also discussed in this article.     

An approximation to the distribution of the product of two dependent correlation coefficients

Many methodological studies depend on the product of two dependent correlation coefficients. However, the behavior of the distribution of the product of two dependent correlation coefficients is not well known. The distribution of sets of correlation coefficients has been well studied, but not the distribution of the product of two dependent correlation coefficients. The present study derives an approximation to the distribution of the product of two dependent correlation coefficients with a closed form, resulting in a Pearson Type I distribution. A simulation study is also conducted to assess the accuracy of the approximation.     

Computational approach test for inference about several correlation coefficients: Equality and common

In this article, we consider inference about the correlation coefficients of several bivariate normal distributions. We first propose computational approach tests for testing the equality of the correlation coefficients. In fact, these approaches are parametric bootstrap tests, and simulation studies show that they perform very satisfactory, and the actual sizes of these tests are better than other existing approaches. We also present a computational approach test and a parametric bootstrap confidence interval for inference about the parameter of common correlation coefficient. At the end, all the approaches are illustrated using two real examples.     

Gini correlation as a measure of monotonicity and two of its usages

In this paper it is shown that the Gini correlation (suggested recently in this Journal) is a special case of a general family of measures of monotonicity. Two new usages of the GINI coefficient will be discussed: 1. for measuring convexity of time series, and 2. for measuring overlapping between groups. The asymptotic variances of the above two measures will be derived.     

Estimates of regression coefficients based on the sign covariance matrix

Summary. A new estimator of the regression parameters is introduced in a multivariate multiple-regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting efficiencies of the SCM regression estimate. The estimate is shown to be consistent with a limiting multinormal distribution. The influence function, as a function of the length of the contamination vector, is shown to be linear in elliptic cases; for the least squares (LS) estimate it is quadratic. The asymptotic relative efficiencies with respect to the LS estimate are given in the multivariate normal as well as the t -distribution cases. The SCM regression estimate is highly efficient in the multivariate normal case and, for heavy-tailed distributions, it performs better than the LS estimate. Simulations are used to consider finite sample efficiencies with similar results. The theory is illustrated with an example.     

Estimators of the multiple correlation coefficient: Local robustness and confidence intervals

Many robust regression estimators are defined by minimizing a measure of spread of the residuals. An accompanying R ²-measure, or multiple correlation coefficient, is then easily obtained. In this paper, local robustness properties of these robust R ²-coefficients are investigated. It is also shown how confidence intervals for the population multiple correlation coefficient can be constructed in the case of multivariate normality.     

On small sample properties of the generalized signed rank and generalized sign tests

The generalized signed rank (GSR) and generalized sign (GS) tests were recently proposed for matched pair studies with censored observations (Woolson and Lechenbruch, 1980). The results provided in that paper were asymptotic, and no indicatin of small sample behavior was given. In this paper we report on simulation studied of these statistics for a variety of distributions. We find that the GSR is more powerful than the GS, and that censoring does not affect power greatly. In the original paper, we assumed each member of the pair has the same censoring time. We consider a variant of this in which each member of the pair has a censoring time chosen from a uniform distribution, and the minimum of these times is selected as the censoring time for the pair. It is found that the power of the test is slightly reduced because the number of doubly censored pairs is increased.     

Randomization with non-uniform allocations: fulfillment time distributions and bias properties

This article compares the properties of two balanced randomization schemes with several treatments under non-uniform allocation probabilities. According to the first procedure, the so-called truncated multinomial randomization design, the process employs a given allocation distribution, until a treatment receives its quota of subjects, after which this distribution switches to the conditional distribution for the remaining treatments, and so on. The second scheme, the random allocation rule, selects at random any legitimate assignment of the given number of subjects per treatment. The behavior of these two schemes is shown to be quite different: the truncated multinomial randomization design's assignment probabilities to a treatment turn out to vary over the recruitment period, and its accidental bias can be large, whereas the random allocation rule's this bias is bounded. The limiting distributions of the instants at which a treatment receives the given number of subjects is shown to be that of weighted spacings for normal order statistics with different variances. Formulas for the selection bias of both procedures are also derived.     

Analysis of generalized semiparametric mixed varying‐coefficients models for longitudinal data

The generalized semiparametric mixed varying‐coefficient effects model for longitudinal data can accommodate a variety of link functions and flexibly model different types of covariate effects, including time‐constant, time‐varying and covariate‐varying effects. The time‐varying effects are unspecified functions of time and the covariate‐varying effects are nonparametric functions of a possibly time‐dependent exposure variable. A semiparametric estimation procedure is developed that uses local linear smoothing and profile weighted least squares, which requires smoothing in the two different and yet connected domains of time and the time‐dependent exposure variable. The asymptotic properties of the estimators of both nonparametric and parametric effects are investigated. In addition, hypothesis testing procedures are developed to examine the covariate effects. The finite‐sample properties of the proposed estimators and testing procedures are examined through simulations, indicating satisfactory performances. The proposed methods are applied to analyze the AIDS Clinical Trial Group 244 clinical trial to investigate the effects of antiretroviral treatment switching in HIV‐infected patients before and after developing the T215Y antiretroviral drug resistance mutation. The Canadian Journal of Statistics 47: 352–373; 2019 © 2019 Statistical Society of Canada     

An estimator of population total in multiple characteristics and its robustness to product moment correlation coefficient

We developed an alternative estimator for the probability proportional to size with replacement sampling scheme when certain characteristics under study have low correlation with the size measured used for sample selection. The performance of the proposed estimator has been studied with other related alternative estimators by comparing biases and the variances of respective alternative estimators. Most of the alternative estimators assume the knowledge of the product moment correlation coefficient. Therefore an empirical study, with the help of wide variety of populations, has been carried out to study their respective efficiency when correlation coefficient is departed from its true value.     

Impact of Contamination on Training and Test Error Rates in Statistical Clustering

The k-means algorithm is one of the most common non hierarchical methods of clustering. It aims to construct clusters in order to minimize the within cluster sum of squared distances. However, as most estimators defined in terms of objective functions depending on global sums of squares, the k-means procedure is not robust with respect to atypical observations in the data. Alternative techniques have thus been introduced in the literature, e.g., the k-medoids method. The k-means and k-medoids methodologies are particular cases of the generalized k-means procedure. In this article, focus is on the error rate these clustering procedures achieve when one expects the data to be distributed according to a mixture distribution. Two different definitions of the error rate are under consideration, depending on the data at hand. It is shown that contamination may make one of these two error rates decrease even under optimal models. The consequence of this will be emphasized with the comparison of influence functions and breakdown points of these error rates.     

On the distribution of the correlation coefficient when sampling from a mixture of two bivariate normal densities: Robustness and the effect of outliers

The distribution of the sample correlation coefficient is derived when the population is a mixture of two bivariate normal distributions with zero mean but different covariances and mixing proportions 1 - λ and λ respectively; λ will be called the proportion of contamination. The test of ρ = 0 based on Student's t, Fisher's z, arcsine, or Ruben's transformation is shown numerically to be nonrobust when λ, the proportion of contamination, lies between 0.05 and 0.50 and the contaminated population has 9 times the variance of the standard (bivariate normal) population. These tests are also sensitive to the presence of outliers.     

A generalized two-piece skew normal distribution and some of its properties

In this paper, we develop a generalized version of the two-piece skew normal distribution of Kim [On a class of two-piece skew-normal distributions, Statistics 39(6) (2005), pp. 537–553] and derive explicit expressions for its distribution function and characteristic function and discuss some of its important properties. Further estimation of the parameters of the generalized distribution is carried out.     

Some moment properties and limit theorems of the reversed generalized logistic distribution with applications

In this paper we discuss an extended form of the logistic distribution and refer to it as the reversed generalized logistic distribution. We study some moment properties, and derive exact and explicit formulas for the mean, median, mode, variance, coefficients of skewness and kurtosis, and percentage points of this distribution. In addition, we study its limiting distributions as the shape parameter tends to zero or infinity. We also discuss some possible applications in bioassays through logistic regression approach.     

The generalized odd log-logistic family of distributions: properties,regression models and applications

We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.