Uniform Asymptotic Expansion of Likelihood Ratio for Markov Dependent Observations

An asymptotic expansion of the logarithm of the likelihood ratio for Markov dependent observation is obtained. A functional limit theorem for the likelihood ratio is proved, which gives a way to study limiting distributions of the likelihood ratio based on stopping times, in particular, that of sequential probability ratio test.     

方差未知时两样本正态混合模型齐-性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

方差未知时两样本正态混合模型齐一性的修正似然比检验

本文讨论了方差未知时检验两样本正态混合模型齐一性的修正似然比统计量的极限性质,证明了原假设下修正似然比统计量的渐近分布为自由度为1的卡方分布.     

Nonnull distributions of two test criteria for independence under local alternatives

For testing the independence of q-sets in a p-variate normal population, the asymptotic distributions of the likelihood ratio test, and the test proposed by the author under local alternatives are derived in terms of noncentral χ² variates.     

关于似然比序随机比较的一些结果

研究了两组随机变量列之间似然比序的随机比较，得到的结果推广了Shaked 和 Shanthikumar (1994) 中的 Theorem 1.C.19 和Theorem 1.C.20.      

两个总体相等的广义似然比检验

利用广义似然比检验的原理,首先求出广义似然比统计量的极限分布,然后给出了两个总体相等的广义似然比检验方法,并且给出了随机模拟结果.     

随机变量独立性的判别方法

归纳总结判别随机变量独立性的方法,并借助实例加以说明.     

Information Criteria in Model Selection for Mixing Processes

We present information criteria for statistical model evaluation problems for stochastic processes. The emphasis is put on the use of the asymptotic expansion of the distribution of an estimator based on the conditional Kullback–Leibler divergence for stochastic processes. Asymptotic properties of information criteria and their improvement are discussed. An application to a diffusion process is presented.     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

随机变量独立性判别方法注记

给出了随机变量 X1 ,X2 ,X3相互独立的一个判定方法 .并将此方法中推广到更一般情形.     

Smoothing of likelihood ratio statistic for equiprobable multinomial goodness-of-fit

The likelihood ratio chi-square criterion for testing goodness-of-fit in k cell multinomials is known to overestimate significance for small and moderate sample sizes (see, e.g., Larntz (1978)). Therefore, the usual chi-square approximation to the upper tail of the likelihood ratio statistic G ², is not satisfactory. Several authors have derived adjustments (e.g., Williams (1976), Smith et al. (1981), Hosmane (1987b)), so that the asymptotic mean of G ² matches the mean of the asymptotic chi-square distribution in the hope that the distribution of G ² would improve. In this paper, a new adjustment to G ² is determined on the basis of the n ^-1-order term (n being the total number) of the Edgeworth expansion of the distribution of smoothed G ². Monte Carlo results indicate that the modified G ² outperforms the unadjusted G ².     

随机向量独立性判别准则及其应用

介绍了随机向量独立性的三种常用判别准则 ,提出了相应的教学法的建议 .     

Information Criteria for Small Diffusions via the Theory of Malliavin–Watanabe

Information criteria based on the expected Kullback–Leibler information are presented by means of the asymptotic expansions derived with the Malliavin calculus. We consider the evaluation problem of statistical models for diffusion processes with small noise. The correction terms are essentially different from the ones for ergodic diffusion models presented in Uchida and Yoshida [34, 35].     

有限混合模型有限制Log极大似然比统计量的极限分布

有限混合模型的Log极大似然比统计量极限分布不是平常x2分布,1985年已为Hartigan指出.在这篇文章我们限制了混合比大于一正数下,讨论了两个含单个未知参数混合模型的Log极大似然比统计量的极限分布,它是零与x2分布的混合分布.     

几个总体均值函数的鞍点逼近

本文发展了几个总体的均值向量的函数的尾部概率的鞍点逼近方法，并应用它于Bootstrap估计中，以代替Monte Carlo模拟，一些数值例子说明了其近似精度。     

多层连锁不平衡的齐一性检验

In this article, using the likelihood score theory extended to nuisance parameters we derive a new homogeneity score test for comparing linage disequilibrium across several strata. Power and sample size formulae are also obtained.     

Convergence Rate of the Distributions of Normalized Maximum Likelihood Estimators for Irregular Parametric Families

We study the convergence rate of the distributions of normalized maximum likelihood estimators defined by a parametric family of discontinuous multidimensional densities in the case of a vector parameter.     

The Fano Plane and the Strong Independence Ratio in Hypergraphs of Maximum Degree 3

A set S of vertices in a hypergraph H is strongly independent if no two vertices in S belong to a common edge. The strong independence number of H, denoted , is the maximum cardinality of a strongly independent set in H. The rank of H is the size of a largest edge in H. The hypergraph H is k‐uniform if every edge of H has size k. The transversal number, denoted , of H is the minimum number of vertices that intersect every edge. Our main result is that for all , the strong independence ratio of a hypergraph H with rank k and maximum degree 3 satisfies and this bound is achieved for all . In particular, this bound is achieved for the Fano plane. As an application of our result, we show that if H is a k‐uniform hypergraph on n vertices with m edges and with maximum degree 3 and vertices of degree 3, then . This improves a result due to Chvátal and McDiarmid [Combinatorica 12 (1992), 19–26] who proved that in the case when is even and H has maximum degree 3.     

Tests for the mean direction of the Langevin distribution with large concentration parameter

In this paper we study the asymptotic behaviors of the likelihood ratio criterion (T_L^(s)), Watson statistic (T_W^(s)) and Rao statistic (T_R^(s)) for testing H_0s: μ (a given subspace) against H_1s: μ , based on a sample of size n from a p-variate Langevin distribution M_p(μ, κ) when κ is large. For the case when κ is known, asymptotic expansions of the null and nonnull distributions of these statistics are obtained. It is shown that the powers of these statistics are coincident up to the order κ⁻¹. For the case when κ is unknown, it is shown that T_R^(s) T_L^(s) T_W^(s) in their powers up to the order κ⁻¹.     

ONE-WAY MULTIVARIATE REPEATED MEASUREMENTS ANALYSIS OF VARIANCE MODEL

The one-way multivariate repeated measurements analysis of variance (1-way MRM ANOVA) model for complete data and the sphericity test are studied.