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线性模型的替代拟合优度检验AI 解读

Fan and Huang (2001) presented a goodness-of-fit test for linear models based on Fourier transformations of the residuals of the fitted model. We present two more theoretically appealing tests in which the Fourier transforms are incorporated into a fitted model. We show that when suitably normalized, the new test statistics have the same asymptotic distribution as Fan and Huang’s test. We propose modifications to the asymptotic normalization constants to improve the small…

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检验线性模型中的独立性假设AI 解读

We propose using an existing set of statistical tools in a new way that allows one to test the independence assumption in standard normal theory linear models. The set of tools is near-replicate lack-of-fit tests. The classical lack-of-fit test requires a linear model in which some rows of the model matrix are repeated. Near-replicate lack-of-fit tests were developed to mimic the behavior of the classical test by identifying clusters of rows in the design matrix that are…

线性模型中独立性假设的检验AI 解读

We propose using an existing set of statistical tools in a new way that allows one to test the independence assumption in standard normal theory linear models. The set of tools is near-replicate lack-of-fit tests. The classical lack-of-fit test requires a linear model in which some rows of the model matrix are repeated. Near-replicate lack-of-fit tests were developed to mimic the behavior of the classical test by identifying clusters of rows in the design matrix that are…

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基于近似重复观测的失拟检验：小样本刻画AI 解读

Several ad hoc tests based on near replicates have been proposed for testing lack of fit in regression analysis. Christensen characterized lack of fit as existing between clusters of near replicates, within clusters, or as a combination of these pure types. Of these, the between-cluster variety is the type commonly associated with the idea of lack of fit. Christensen examined a test that was new to the normal theory regression literature and established uniformly most…

用普通最小二乘分析两阶段抽样数据AI 解读

A reasonably broad class of models for analyzing two-stage samples is considered. For models in this class, ordinary least squares (OLS) estimates are best linear unbiased estimates (BLUE's) and a large variety of exact tests and confidence intervals are available. The necessary computations can be made simply by fitting two models in the ordinary fashion using least squares. The most stringent assumption made is that there are equal numbers of observations taken in each…

Dirichlet过程下不可回溯序贯抽样的有限停止AI 解读

This paper shows that for sequential sampling without recall from a Dirichlet process, there exists a finite bound beyond which one will cease sampling with probability 1. The result is valid for Dirichlet processes defined on closed bounded intervals of the real line.

两阶段抽样中普通最小二乘方法的一则说明AI 解读

A class of linear models for two-stage sampling problems is considered. Ordinary least squares estimates are optimal for these models. For some parameters the usual least squares estimates of standard errors are shown to be appropriate.

利用狄利克雷过程混合估计二项分布参数AI 解读

The theory of Dirichlet processes is applied to the empirical Bayes estimation problem in the binomial case. The approach is Bayesian rather than being empirical Bayesian. When the prior is a Dirichlet process the posterior is a mixture of Dirichlet processes. Explicit estimators are given for the case of 2 and 3 parameters and compared with other empirical Bayes estimators by way of examples. Since the number of calculations become enormous when the number of parameters…