A pivot function and its limiting distribution: applications in goodness of fit and testing hypothesis

ABSTRACT

In this paper, a pivot function which is in terms of the sample and the underlying population distribution is introduced. It is assumed that the population distribution is continuous and strictly increasing on its support. Then, the martingale central limit theorem is applied to prove that limiting distribution of the pivot function is the standard normal. Interestingly, this result provides a unified procedure that can be applied for the goodness of fit, and for the purpose of parametric and nonparametric inferences, for the populations having distribution functions that are continuous and strictly increasing on their supports. The method is fairly simple and can be easily applied.     

A Bayesian panel data framework for examining the economic growth convergence hypothesis: do the G7 countries converge?

In this paper, we suggest a Bayesian panel (longitudinal) data approach to test for the economic growth convergence hypothesis. This approach can control for possible effects of initial income conditions, observed covariates and cross-sectional correlation of unobserved common error terms on inference procedures about the unit root hypothesis based on panel data dynamic models. Ignoring these effects can lead to spurious evidence supporting economic growth divergence. The application of our suggested approach to real gross domestic product panel data of the G7 countries indicates that the economic growth convergence hypothesis is supported by the data. Our empirical analysis shows that evidence of economic growth divergence for the G7 countries can be attributed to not accounting for the presence of exogenous covariates in the model.     

The power of generalized odds ratio in assessing association in genetic studies with known mode of inheritance

The generalized odds ratio (OR_G) is a novel model-free approach to test the association in genetic studies by estimating the overall risk effect based on the complete genotype distribution. However, the power of OR_G has not been explored and, particularly, in a setting where the mode of inheritance is known. A population genetics model was simulated in order to define the mode of inheritance of a pertinent gene–disease association in advance. Then, the power of OR_G was explored based on this model and compared with the chi-square test for trend. The model considered bi- and tri-allelic gene–disease associations, and deviations from the Hardy–Weinberg equilibrium (HWE). The simulations showed that bi- and tri-allelic variants have the same pattern of power results. The power of OR_G increases with increase in the frequency of mutant allele and the coefficient of selection and, of course, the degree of dominance of the mutant allele. The deviation from HWE has a considerable impact on power only for small values of the above parameters. The OR_G showed superiority in power compared with the chi-square test for trend when there is deviation from HWE; otherwise, the pattern of results was similar in both the approaches.     

Evaluation of false discovery rate and power via sample size in microarray studies

Microarray studies are now common for human, agricultural plant and animal studies. False discovery rate (FDR) is widely used in the analysis of large-scale microarray data to account for problems associated with multiple testing. A well-designed microarray study should have adequate statistical power to detect the differentially expressed (DE) genes, while keeping the FDR acceptably low. In this paper, we used a mixture model of expression responses involving DE genes and non-DE genes to analyse theoretical FDR and power for simple scenarios where it is assumed that each gene has equal error variance and the gene effects are independent. A simulation study was used to evaluate the empirical FDR and power for more complex scenarios with unequal error variance and gene dependence. Based on this approach, we present a general guide for sample size requirement at the experimental design stage for prospective microarray studies. This paper presented an approach to explicitly connect the sample size with FDR and power. While the methods have been developed in the context of one-sample microarray studies, they are readily applicable to two-sample, and could be adapted to multiple-sample studies.     

Intrinsic Bayesian inference on a Poisson rate and on the ratio of two Poisson rates

Our purpose is to explore the intrinsic Bayesian inference on the rate of a Poisson distribution and on the ratio of the rates of two independent Poisson distributions, with the natural conjugate family of priors in the first case and the semi-conjugate family of priors defined by Laurent and Legrand (2011) in the second case. Intrinsic Bayesian inference is derived from the Bayesian decision theory framework based on the intrinsic discrepancy loss function. We cover in particular the case of some objective Bayesian procedures suggested by Bernardo when considering reference priors.     

Sequential analysis methodology for a Poisson GLMM with applications to multicenter randomized clinical trials

Sequential analyses in clinical trials have ethical and economic advantages over fixed sample size methods. The sequential probability ratio test (SPRT) is a hypothesis testing procedure which evaluates data as it is collected. The original SPRT was developed by Wald for one-parameter families of distributions and later extended by Bartlett to handle the case of nuisance parameters. However, Bartlett's SPRT requires independent and identically distributed observations. In this paper we show that Bartlett's SPRT can be applied to generalized linear model (GLM) contexts. Then we propose an SPRT analysis methodology for a Poisson generalized linear mixed model (GLMM) that is suitable for our application to the design of a multicenter randomized clinical trial that compares two preventive treatments for surgical site infections. We validate the methodology with a simulation study that includes a comparison to Neyman–Pearson and Bayesian fixed sample size test designs and the Wald SPRT.     

空间计量经济学理论体系的解析及其展望

随着空间经济理论研究出现重大突破,空间计量经济学也从边缘走向现代计量经济学的主流。重点对空间计量经济模型的设立包括空间横截面数据模型、空间面板数据模型以及空间离散数据模型进行讨论,对模型参数估计方法包括最大似然估计法、两阶段最小二乘法和矩估计法等进行分析,对模型检验方法包括Moran’s I方法和LM/RS方法等内容进行总结,最后展望了该理论研究未来的发展趋势。     

COMBINING INDIVIDUAL PARTICIPANT DATA AND SUMMARY STATISTICS FROM BOTH CONTINUOUSLY VALUED AND BINARY VARIABLES TO ESTIMATE REGRESSION PARAMETERS

Recent research has extended standard methods for meta‐analysis to more general forms of evidence synthesis, where the aim is to combine different data types or data summaries that contain information about functions of multiple parameters to make inferences about the parameters of interest. We consider one such scenario in which the goal is to make inferences about the association between a primary binary exposure and continuously valued outcome in the context of several confounding exposures, and where the data are available in various different forms: individual participant data (IPD) with repeated measures, sample means that have been aggregated over strata, and binary data generated by thresholding the underlying continuously valued outcome measure. We show that an estimator of the population mean of a continuously valued outcome can be constructed using binary threshold data provided that a separate estimate of the outcome standard deviation is available. The results of a simulation study show that this estimator has negligible bias but is less efficient than the sample mean – the minimum variance ratio is based on a Taylor series expansion. Combining this estimator with sample means and IPD from different sources (such as a series of published studies) using both linear and probit regression does, however, improve the precision of estimation considerably by incorporating data that would otherwise have been excluded for being in the wrong format. We apply these methods to investigate the association between the G277S mutation in the transferrin gene and serum ferritin (iron) levels separately in pre‐ and post‐menopausal women based on data from three published studies.