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针对中心混合备择的同质性检验AI 解读

A test of homogeneity is derived for a general sampling model. The alternative hypothesis is a mixture over a parameter of the sampling model, centered at the null hypothesis. The test statistic is derived through a score test. Its functional form is independent of the particular mixing distribution. Suppose Yi (i = 1, …, n) are independent random variables with respective probability density (or mass) functions fi (yi ‖ λi). Under the null hypothesis, suppose all λ i…

极限密度函数的渐近正态性及其贝叶斯含义AI 解读

SUMMARY Precise statements of three basic conditions for the asymptotic normality of limiting density functions are given. In the Bayesian context, these conditions as a whole provide a greater generality and more operational flexibility for asymptotic posterior normality than those assumed by previous investigators.

回归模型的得分检验AI 解读

Many score statistics used for testing trends in means, either based on the observed values of the response variables or their ranks, can be expressed in terms of quadratic forms. This article explores systematically the robustness of optimality of these statistics, as well as the optimal properties of the associated tests.

通过潜变量估计实现多指标多原因模型的 EM 方法AI 解读

This article considers both likelihood and Bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable. The model is complicated by its reduced form, which displays a mixture of econometric and psychometric themes. We avoid this complexity via the estimation of the unobservable latent variable through direct use of the original structural form. This approach not only provides maximum likelihood estimates…

正态离散矩阵的贝叶斯推断及其在随机多元回归中的应用AI 解读

Summary This paper discusses Bayesian inference procedures for a normal dispersion matrix. Structural information for the prior mean of the dispersion matrix is incorporated into the analysis through a Normal-Wishart prior distribution. Many of the resulting Bayes estimates are invariant, consistent and asymptotically efficient. Using this procedure, a coherent Bayesian argument for stochastic multiple regression analysis is developed, where dependent and independent…