论文检索

非中心卡方分布非中心参数的估计AI 解读

Let $X$ be distributed according to a non-central Chi squared distribution with $p$ degrees of freedom. The non-central Chi squared distribution arises in various statistical analyses and the estimation of the non-centrality parameter is of importance in some problems. This paper deals with the admissibility of certain estimates of the non-centrality parameter. It is shown that $(X - p)^+$, the positive part of $X - p$ dominates the maximum likelihood estimator with squared…

多项分布的极化检验AI 解读

A multinomial distribution with k cells is said to be polarized if the total probability mass of the distribution is essentially concentrated into a fewer number of cells. In this article a criterion is developed for measuring polarization, and a statistical test is given for testing the hypothesis that a multinomial distribution has a given measure of polarization against the alternative hypothesis that the measure of polarization is larger. The given test is called a…

多项分布的极化检验AI 解读

A multinomial distribution with k cells is said to be polarized if the total probability mass of the distribution is essentially concentrated into a fewer number of cells. In this article a criterion is developed for measuring polarization, and a statistical test is given for testing the hypothesis that a multinomial distribution has a given measure of polarization against the alternative hypothesis that the measure of polarization is larger. The given test is called a…

多项分布概率的估计AI 解读

This paper deals with the estimation of the parameters (cell probabilities) of a multinomial distribution. For the binomial distribution it is known that the maximum likelihood estimator (MLE) is admissible with respect to the squared error loss. It is shown that the MLE is admissible also in the case of the multinomial distribution.

若干非参数随机性检验AI 解读

Let {Xj } be a sequence of independently distributed real valued random variables, and let Rj denote the rank of Xj among X 1, ···, Xj for j = 1, ···, n. The Rj 's are called “sequential ranks.” A class of unbiased tests, based on the sequential ranks, is given for testing the hypothesis that the random variables are identically distributed against the alternative hypothesis that they are stochastically ordered.

若干非参数随机性检验AI 解读

Let {Xj } be a sequence of independently distributed real valued random variables, and let Rj denote the rank of Xj among X 1, ···, Xj for j = 1, ···, n. The Rj 's are called “sequential ranks.” A class of unbiased tests, based on the sequential ranks, is given for testing the hypothesis that the random variables are identically distributed against the alternative hypothesis that they are stochastically ordered.

多元正态均值的一族可容许极小极大估计量AI 解读

Let the $p$-component vector $X$ be normally distributed with mean $\xi$ and covariance $\sigma^2I$ where $I$ denotes the identity matrix and $\sigma$ is known. For estimating $\xi$ with quadratic loss, it is known that $X$ is minimax but inadmissible for $p \geqq 3$. We obtain a family of estimators which dominate $X$ and are admissible. These estimators are, therefore, both minimax and admissible.