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多元模型中单侧备择的方向性检验AI 解读

Consider one-sided testing problems for a multivariate exponential family model. Through conditioning or other considerations, the problem oftentimes reduces to testing a null hypothesis that the natural parameter is a zero vector against the alternative that the natural parameter lies in a closed convex cone $\mathscr{C}$. The problems include testing homogeneity of parameters, testing independence in contingency tables, testing stochastic ordering of distributions and many…

同质性检验的无偏性AI 解读

Let $X_i, i = 1, 2, \ldots, k$, be independent random variables distributed according to a one-parameter exponential family with parameter $\theta_i$. Assume also that the probability density function of $X_i$ is a Polya frequency function of order two $(PF_2)$. Consider the null hypothesis $H_0: \theta_1 = \theta_2 = \cdots = \theta_k$ against the alternative $K$: not $H_0$. We show that any permutation invariant test of size $\alpha$, whose conditional (on $T = \sum^k_{i = 1}X_i)$…

二项分布双重抽样估计的若干结果AI 解读

A complete class result is obtained for double sample estimation of a binomial parameter. The complete class leads to some inadmissibility results for some procedures that are likely to be used in practice. It is also shown that the sample proportion as a true double estimator is not unbiased.

贝叶斯两阶段抽样估计程序AI 解读

Bayes double sample procedures are given for estimating the mean of exponential family distributions. The distribution can be multiparameter and so the case of normal mean with unknown variance is included. Linear combination loss functions are usually assumed. Stein's double sample procedure, and other intuitive double sample procedures for estimating a binomial parameter, are studied. Recommendations are given, including guidelines for the size of the initial samples.

两个正态分布共同均值的估计AI 解读

Consider the problem of estimating the common mean of two normal distributions. Two new unbiased estimators of the common mean are offered for the equal sample size case. Both are better than the sample mean based on one population for sample sizes of 5 or more. A slight modification of one of the estimators is better than either sample mean simultaneously for sample sizes of 10 or more. This same estimator has desirable large sample properties and an explicit simple upper…