Estimation of a Conditional Copula and Association Measures

Abstarct. This paper is concerned with studying the dependence structure between two random variables Y ₁ and Y ₂ conditionally upon a covariate X. The dependence structure is modelled via a copula function, which depends on the given value of the covariate in a general way. Gijbels et al. (Comput. Statist. Data Anal., 55, 2011, 1919) suggested two non‐parametric estimators of the ‘conditional’ copula and investigated their numerical performances. In this paper we establish the asymptotic properties of the proposed estimators as well as conditional association measures derived from them. Practical recommendations for their use are then discussed.     

中国农村金融发展与农村居民收入增长关系的经验研究

基于1978-2007年的相关数据,运用Johansen协整检验、格兰杰因果关系检验、脉冲响应函数和方差分解等方法对中国农村金融发展与农村居民收入增长关系进行检验。研究认为：农村金融发展与农村居民收入增长存在长期协整关系,并且只是存在单向因果关系。     

Construction and selection of tightened–normal–tightened variables sampling scheme of type TNTVSS (n 1, n 2; k)

This paper provides tables for the construction and selection of tightened–normal–tightened variables sampling scheme of type TNTVSS (n ₁, n ₂; k). The method of designing the scheme indexed by (AQL, α) and (LQL, β) is indicated. The TNTVSS (n _T , n _N; k) is compared with conventional single sampling plans for variables and with TNT (n ₁, n ₂; c) scheme for attributes, and it is shown that the TNTVSS is more efficient.     

Four tests of fit for the beta-binomial distribution

Tests based on the Anderson–Darling statistic, a third moment statistic and the classical Pearson–Fisher X ² statistic, along with its third-order component, are considered. A small critical value and power study are given. Some examples illustrate important applications.     

Some tests for uniformity of circular distributions powerful against multimodal alternatives

The author introduces new statistics suited for testing uniformity of circular distributions and powerful against multimodal alternatives. One of them has a simple expression in terms of the geometric mean of the sample of chord lengths. The others belong to a family indexed by a continuous parameter. The asymptotic distributions under the null hypothesis are derived. We compare the power of the new tests against Stephens's alternatives with those of Ajne, Watson, and Hermans‐Rasson's tests. Some of the new tests are the most powerful when the alternative has three or four modes. A heuristic justification of this feature is given. An application to the analysis of archaeological data is provided. The Canadian Journal of Statistics 38:80–96; 2010 © 2010 Statistical Society of Canada     

An adaptive allocation sampling design for which the conventional stratified estimator is an appropriate estimator

Adaptive allocations in stratified sampling design are suitable for studying Biological and Environmental populations. Biologists tend to use the conventional stratified estimator for an adaptive allocation sampling design in spite of its adaptive nature. In this paper, we have introduced an adaptive allocation sampling design for which the conventional stratified estimator has some desired statistical properties. We conduct a simulation study on a real population. The results show that the conventional stratified estimator for the introduced adaptive allocation sampling design is more efficient than other available estimators.     

A note on estimating the false discovery rate under mixture model

In this note, we focus on estimating the false discovery rate (FDR) of a multiple testing method with a common, non-random rejection threshold under a mixture model. We develop a new class of estimates of the FDR and prove that it is less conservatively biased than what is traditionally used. Numerical evidence is presented to show that the mean squared error (MSE) is also often smaller for the present class of estimates, especially in small-scale multiple testings. A similar class of estimates of the positive false discovery rate (pFDR) less conservatively biased than what is usually used is then proposed. When modified using our estimate of the pFDR and applied to a gene-expression data, Storey's q-value method identifies a few more significant genes than his original q-value method at certain thresholds. The BH like method developed by thresholding our estimate of the FDR is shown to control the FDR in situations where the p  -values have the same dependence structure as required by the BH method and, for lack of information about the proportion _π0${\pi }_0$ of true null hypotheses, it is reasonable to assume that _π0${\pi }_0$ is uniformly distributed over (0,1).     

Re-parameterization of multinomial distributions and diversity indices

It is shown in this paper that the parameters of a multinomial distribution may be re-parameterized as a set of generalized Simpson's diversity indices. There are two important elements in the generalization: (1) Simpson's diversity index is extended to populations with infinite species; (2) weighting schemes are incorporated. A class of unbiased estimators for the generalized Simpson's biodiversity indices is proposed. Asymptotic normality is established for the estimators. Both the unbiasedness and the asymptotic normality of the estimators hold for all three cases of the number of species in the population: infinite, finite and known, and finite but unknown. In the case of a population with a finite number of species, known or unknown, it is also established that the proposed estimators are uniformly minimum variance unbiased and are asymptotically efficient.     

The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference

We consider the case of a multicenter trial in which the center specific sample sizes are potentially small. Under homogeneity, the conventional procedure is to pool information using a weighted estimator where the weights used are inverse estimated center-specific variances. Whereas this procedure is efficient for conventional asymptotics (e. g. center-specific sample sizes become large, number of center fixed), it is commonly believed that the efficiency of this estimator holds true also for meta-analytic asymptotics (e.g. center-specific sample size bounded, potentially small, and number of centers large). In this contribution we demonstrate that this estimator fails to be efficient. In fact, it shows a persistent bias with increasing number of centers showing that it isnot meta-consistent. In addition, we show that the Cochran and Mantel-Haenszel weighted estimators are meta-consistent and, in more generality, provide conditions on the weights such that the associated weighted estimator is meta-consistent.     

Discovering influential cases in linear regression with MINITAB: Peeking into multidimensions with a MINITAB macro

Various diagnostic statistics have been proposed to help identify cases that markedly affect, or influence, the features of a fitted linear regression model. Once influential cases are found, decisions can be made regarding their worth in the model building process. Since a subject data set may contain both singly influential cases and influential multiple case subsets, the capability to assess the joint influence of cases is needed for a complete analysis. The aim of this work is to briefly review Cook’s distance measure for multiple cases, an effective diagnostic for this purpose, and present a method using it to search for influential multiple case subsets. The method is applied in two example analyses by way of a MINITAB Statistical Software macro.