A new estimator of entropy and its application in testing normality

In this paper, we introduce a new estimator of entropy of a continuous random variable. We compare the proposed estimator with the existing estimators, namely, Vasicek [A test for normality based on sample entropy, J. Roy. Statist. Soc. Ser. B 38 (1976), pp. 54–59], van Es [Estimating functionals related to a density by class of statistics based on spacings, Scand. J. Statist. 19 (1992), pp. 61–72], Correa [A new estimator of entropy, Commun. Statist. Theory and Methods 24 (1995), pp. 2439–2449] and Wieczorkowski-Grzegorewski [Entropy estimators improvements and comparisons, Commun. Statist. Simulation and Computation 28 (1999), pp. 541–567]. We next introduce a new test for normality. By simulation, the powers of the proposed test under various alternatives are compared with normality tests proposed by Vasicek (1976) and Esteban et al. [Monte Carlo comparison of four normality tests using different entropy estimates, Commun. Statist.–Simulation and Computation 30(4) (2001), pp. 761–785].     

Some Bounds on the Distribution of Certain Quadratic Forms in Normal Random Variables

The paper derives bounds on the distribution of the quadratic forms Z = y ^H( X Γ X ^H)⁻¹ y and W = y ^H(σ² I + X Γ X ^H)⁻¹ y , where the elements of the M × 1 vector y and the M × N matrix X are independent identically distributed (i.i.d.) complex zero mean Normal variables, Γ is some N × N diagonal matrix with positive diagonal elements, I , is the identity, σ² is a constant and ^H denotes the Hermitian transpose. The bounds are convenient for numerical work and appear to be tight for small values of M . This work has applications in digital mobile radio for a specific channel where M antennas are used to receive a signal with N interferers. Some of these applications in radio communication systems are discussed.     

On the robustness of the power function of the one-sample test for the negative exponential distribution

The robustness of the power function of the standard one-sample parametric test for the mean of the negative exponential distribution is examined. The main form of departure from the exponential assumption is a mixture of negative exponential components although an alternative Gamma distribution is also examined. It is found that the test is sensitive to these departures although the effect of mixtures with short tails is less dramatic than those with long tails.     

A modified chi-square test of independence against a class of ordered alternatives in an r x c contingency table

A modified chi-square test statistic is constructed for testing the hypothesis of independence in a two-way contingency table against a class of ordered alternatives defined in terms of pooled cross-product ratios. The test procedure can also be used to test for positive quadrant dependence in a two-way contingency table. The asymptotic distribution of the test statistic under the null hypothesis is obtained. Some power comparisons with known test procedures are given. A numerical example is given to illustrate the use of this test.     

Diagnostics for Autocorrelated Regression Models

This paper discusses the local influence approach to the linear regression model with AR(1) errors. Diagnostics for the autocorrelation models and for the autocorrelation coefficient only are proposed and developed respectively, when simultaneous perturbations of the response vector are allowed. Furthermore, the direction of maximum curvature of local influence analysis is shown to be exactly the same as that in Tsai & Wu (1992) when only the autocorrelation coefficient is of special interest.     

判别分析统计检验体系的探讨

判别分析已越来越受到人们的重视并取得了重要的应用成果,但应用中存在着简单套用的情况,对判别分析的适用性、判别效果的显著性、判别变量的判别能力以及判别函数的判别能力的检验等问题重视不够。为了更好地应用判别分析,就应对判别分析进行统计检验并建立统计检验体系,统计检验体系应包括：判别分析适用性检验,判别效果显著性检验,判别变量的判别能力检验和判别函数的判别能力检验。     

Locally optimal test of normality against skew-normality

Efficient Score testing procedures for testing for the skewness parameter of the one-parameter and three-parameter skew-normal distributions are investigated. Approximate percentage points for the test statistics are obtained via the Monte Carlo method. Salvan's locally optimal test is extended and simulation is used to show that the power of the extended test is higher than that of the skewness test.     

Bivariate zero-inflated generalized Poisson regression model with flexible covariance

This paper introduces several forms of nested bivariate zero-inflated generalized Poisson (BZIGP) regression model which can be fitted to bivariate and zero-inflated count data. The main advantage of having several forms of BZIGP regression model is that they are nested and allow likelihood ratio test to be performed for choosing the best model. In addition, the BZIGP regression models have flexible forms of marginal mean–variance relationship, can be fitted to bivariate and zero-inflated count data with positive or negative correlations, and allow additional overdispersion of the two response variables. The BZIGP regression models are fitted to the Australian Health Survey data.     

对应分析统计检验体系探讨

对应分析因其结果的易读性,近些年得到了越来越广泛的应用。为了更好地应用对应分析,提出建立对应分析统计检验体系,包括对应分析适用性的统计检验以及对应分析效果的检验,同时还提出应用对应分析时应注意的其它问题。     

A Five-Decision Testing Procedure to Infer the Value of a Unidimensional Parameter

ABSTRACT

A statistical test can be seen as a procedure to produce a decision based on observed data, where some decisions consist of rejecting a hypothesis (yielding a significant result) and some do not, and where one controls the probability to make a wrong rejection at some prespecified significance level. Whereas traditional hypothesis testing involves only two possible decisions (to reject or not a null hypothesis), Kaiser’s directional two-sided test as well as the more recently introduced testing procedure of Jones and Tukey, each equivalent to running two one-sided tests, involve three possible decisions to infer the value of a unidimensional parameter. The latter procedure assumes that a point null hypothesis is impossible (e.g., that two treatments cannot have exactly the same effect), allowing a gain of statistical power. There are, however, situations where a point hypothesis is indeed plausible, for example, when considering hypotheses derived from Einstein’s theories. In this article, we introduce a five-decision rule testing procedure, equivalent to running a traditional two-sided test in addition to two one-sided tests, which combines the advantages of the testing procedures of Kaiser (no assumption on a point hypothesis being impossible) and Jones and Tukey (higher power), allowing for a nonnegligible (typically 20%) reduction of the sample size needed to reach a given statistical power to get a significant result, compared to the traditional approach.