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广义置信区间AI 解读

The definition of a confidence interval is generalized so that problems such as constructing exact confidence regions for the difference in two normal means can be tackled without the assumption of equal variances. Under certain conditions, the extended definition is shown to preserve a repeated sampling property that a practitioner expects from exact confidence intervals. The proposed procedure is also applied to the problem of constructing confidence intervals for the…

异方差下的 Chow 型检验AI 解读

Inference for structural parameters that are common to several regressions is a frequent problem of statistical practice. In the unlikely case that the residual error variances are equal for all regressions, the inference problem usually has a closed-form solution within the standard regression framework. In the case of unequal and unknown residual error variances, the problem falls into the category of Behrens-Fisher problems. This article describes a comprehensive solution…

存在干扰参数时假设显著性检验的广义 p 值AI 解读

This article examines some problems of significance testing for one-sided hypotheses of the form H 0 : θ ≤ θ 0 versus H 1 : θ > θ 0, where θ is the parameter of interest. In the usual setting, let x be the observed data and let T(X) be a test statistic such that the family of distributions of T(X) is stochastically increasing in θ. Define Cx as {X : T(X) — T(x) ≥ 0}. The p value is p(x) = sup θ≤θ0 Pr(X ∈ Cx | θ). In the presence of a nuisance parameter η, there may not exist…

多元 Behrens–Fisher 问题的贝叶斯解法AI 解读

We consider the problem of finding the posterior probabilities of ellipsoids for the difference between two multivariate normal means. We do not require the two population covariance matrices to be equal, therefore, our results pertain to the multivariate Behrens—Fisher problem. A Hotelling T 2-like quantity is defined, and its cdf is expressed as a linear combination of the cdf's of some F distributions. This representation enables us to compute desired probabilities…

On obtient un test exact, similaire a celui de Chow (1960), qui comporte une simple integration unidimensionnelle

广义残差方差的最优完全等变估计量的不可容许性AI 解读

The estimation of the generalized residual variance is considered when an observable Wishart random matrix is available. It is shown that when the loss function is normalized squared error, the natural fully equivariant estimator is dominated by an alternative. The latter uses either one of two estimators depending on the result of a preliminary test of significance. This alternate estimator has an everywhere smaller mean normalized squared error than the natural estimator.