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局部中心极限定理、拒绝抽样的高阶相关性与逻辑似然渐近性质AI 解读

Let I1,…,In be independent but not necessarily identically distributed Bernoulli random variables, and let Xn=∑j=1nIj. For ν in a bounded region, a local central limit theorem expansion of $\mathbb {P}(X_{n}=\mathbb {E}X_{n}+\nu)$ is developed to any given degree. By conditioning, this expansion provides information on the high-order correlation structure of dependent, weighted sampling schemes of a population E (a special case of which is simple random sampling), where a…

Cox 回归模型中嵌套病例对照抽样的渐近理论AI 解读

By providing a probabilistic model for nested case-control sampling in epidemiologic cohort studies, consistency and asymptotic normality of the maximum partial likelihood estimator of regression parameters in a Cox proportional hazards model can be derived using process and martingale theory as in Andersen and Gill. A general expression for the asymptotic variance is given and used to calculate asymptotic relative efficiencies relative to the full cohort variance in some…

利用傅里叶级数检验含干扰参数的分布假设AI 解读

We develop a class of smoothed χ 2 tests of distributional hypotheses based on Fourier coefficients used in the density estimation procedure of Fellner. Starting with the simple test of Fx = G, where G is a completely specified hypothesized continuous distribution, we develop tests of the composite null hypothesis Fx − Gα for some vector of unknown parameters α. Variances used in computing the tests vary according to the choice of distributional family and depend on…

利用傅里叶级数检验含干扰参数的分布假设AI 解读

We develop a class of smoothed χ 2 tests of distributional hypotheses based on Fourier coefficients used in the density estimation procedure of Fellner. Starting with the simple test of Fx = G, where G is a completely specified hypothesized continuous distribution, we develop tests of the composite null hypothesis Fx − Gα for some vector of unknown parameters α. Variances used in computing the tests vary according to the choice of distributional family and depend on…

摘要暂缺

基于修正似然的 1∶J 匹配病例对照研究效应检验AI 解读

A test of an effect in matched case-control studies, natural in an analysis of variance context, compares within matched set case-control mean differences to the within matched set variances after removing the case-control effect. For large odds ratios, heuristic reasoning suggests that this new test should be more powerful than the standard score test when two or more controls are matched to any case. Asymptotic theory confirms this in some important situations. Simulation…