Score tests for zero inflation in generalized linear models

The authors develop score tests of goodness of fit for discrete generalized linear models against zero inflation. The binomial and Poisson models are treated as examples, and in the latter case the proposed test reduces to that of Broek (1995). Some simulation results and an illustrative example are presented.     

Testing for bivariate normality using the empirical distribution function

The problem of testing for bivariate normality using the empirical distribution function is considered. A Cramér-von Mises type statistic is defined and asymptotic percentage points for this statistic given. This involves solving a two-dimensional homogeneous integral equation. Unfortunately the Cramér-von Mises statistic is not invariant under orthogonal transformations of the data so that an invariant statistic is developed. Approximations for the distribution of this statistic are found by Monte Carlo. Applications of the statistics are given. It is shown that the statistics are particularly sensitive to certain kinds of pattern in the data and they could be useful in data analysis apart from providing a formal test of bivariate normality     

A comparison of tests of homogeneity for sparse contingency tables

Five tests of homogeneity for a 2x(k+l) contingency table are compared using Monte Carlo techniques. For these studiesit is assumed that k becomes large in such a way that thecontingency table is sparse for 2xk of the cells, but the sample size in two of the cells remains large. The test statistics studied are: the chi-square approximation to the Pearson test statistic, the chi-square approximation to the likelihood ratio statistic, the normal approximation to Zelterman's (1984)the normal approximation to Pearson's chi-square, and the normal approximation to the likelihood ratio statistic. For the range of parameters studied the chi-square approximation to Pearson's statistic performs consistently well with regard to its size and power.     

Quality of Fit Measures in the Framework of Quantile Regression

Abstract. In regression experiments, to learn about the strength of the relationship between a covariate vector and a dependent variable, we propose a ‘coefficient of determination’ based on the quantiles. Such a coefficient is a ‘local’ measure in the sense that the strength is measured at a prespecified quantile level. Once estimated, it can be used, for example, to measure the relative importance of a subset of covariates in the quantile regression context. Related to this coefficient, we also propose a new ‘local’ lack‐of‐fit measure of a given parametric model. We provide some asymptotic results of the proposed measures and carry out a Monte Carlo simulation study to illustrate their use and performance in practice.     

Preliminary test of fit in a general class of conditionally heteroscedastic nonlinear time series

This article is concerned with a general class of conditionally heteroscedastic time series including possibly nonlinear and asymmetric autoregressive conditional heteroscedastic (ARCH) and generalized ARCH models. A problem of preliminary test of fit (PTF, hereafter) within the broad class under consideration is discussed. It is noted that contrary to usual tests in the literature of conditionally heteroscedastic time series, PTF does not require any specification of the conditional variance in advance. Based on the joint limit distributions of sample autocorrelations, a certain Portmanteau-type statistic for PTF is proposed, and its limit is shown to be a chi-square distribution. In addition, some simulation studies, under various innovations, are reported to support our theoretical results.     

Empirical behavior of some tests for normality

The behavior of a range of tests assessing the normality of a sequence of independent and identically distributed random variables is investigated.An examination of the empirical significance level of the tests is undertaken for different sample sizes. The empirical power associated with these tests is also calculated under some alternative distributions.     

A Correlation Test for Normality Based on the Lévy Characterization

A powerful test of fit for normal distributions is proposed. Based on the Lévy characterization, the test statistic is the sample correlation coefficient of normal quantiles and sums of pairs of observations from a random sample. Since the test statistic is location-scale invariant, critical values can be obtained by simulation without estimating any parameters. It is proved that this test is consistent. A power comparison study including some directed tests shows that the proposed test is competitive, it is more powerful than the well-known Jarque–Bera test, and it is comparable to Shapiro–Wilk test against a number of alternatives.     

金额/比率陈述方式和调节匹配对消费者购买意愿的影响

研究引入调节匹配这个源于心理学的概念,探讨两种不同目标导向——求成与避败的消费者面对两种不同的信息陈述方式——金额与比率时对购买意愿的影响。结果表明：信息陈述方式与消费者目标导向产生匹配,才能对消费者态度及其购买意愿产生积极的正面影响;消费者动机存在干扰效果,尤其在消费者属于高动机的情况下,原本对促销信息陈述没有匹配的消费者转变为匹配,且消费者态度明显提升。