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向量值二元失效率的非参数估计AI 解读

Let $\mathbf{X} = (X_1, X_2)'$ be a bivariate random vector distributed according to an absolutely continuous distribution function $F(\mathbf{x})$ which has first partial derivatives. Let $\bar{F}(\mathbf{x}) = P(X_1 > x_1, X_2 > x_2).$ The vector-valued bivariate failure rate is defined as $\mathbf{r}(\mathbf{x}) = (r_1(\mathbf{x}), r_2(\mathbf{x}))',$ where $r_i(\mathbf{x}) = -\partial \ln \bar{F}(\mathbf{x})/\partial x_i (i = 1, 2)$. In this paper, we propose a smooth…

一个变量存在缺失时的均值相等检验：蒙特卡洛研究AI 解读

This article is concerned with the relative merit of the procedures proposed by Lin [2], Metha and Gurland [3], and Morrison [5] for testing the equality of means of a bivariate normal distribution with correlation ρ and common variance σ2 when some observations on one variable are missing. A Monte Carlo study of the powers and level of significance is conducted. Comparisons among these tests and the paired t test are made. The preferred test is established for each…

经验贝叶斯估计问题的收敛速度：连续情形AI 解读

In this paper we construct sequences of estimators for a density function and its derivatives, which are not assumed to be uniformly bounded, using classes of kernel functions. Utilizing these estimators, a sequence of empirical Bayes estimators is proposed. It is found that this sequence is asymptotically optimal in the sense of Robbins (Ann. Math. Statist. 35 (1964) 1-20). The rates of convergence of the Bayes risks associated with the proposed empirical Bayes estimators…

Wilcoxon 检验对某类样本间依赖的稳健性AI 解读

Robustness properties of the two-sample Wilcoxon test are established when the assumption of independence between samples is weakened to allow pairing. In particular, the test is shown to be (asymptotically) conservative when the bivariate distribution governing the pairing is positively quadrant dependent.

不完整数据下均值差异的检验程序AI 解读

Procedures for testing the difference of means are obtained in sampling from a bivariate normal distribution with covariance matrix Σ when some of the observations on one of the variables are missing. A UMP test procedure is obtained when Σ is known. When Σ is not known, exact test procedures may be obtained by discarding partial data. To make use of all available data, approximate test procedures are proposed. These procedures are compared to the exact tests, obtained by…

协方差矩阵未知时多元正态均值的广义贝叶斯极小极大估计AI 解读

Let $\mathbf{X}$ be a $p$-variate $(p \geqq 3)$ vector normally distributed with mean $\mathbf{\theta}$ and covariance matrix $\Sigma$, positive definite but unknown. Let $A$ be a $p \times p$ Wishart matrix with parameters $(n, \Sigma)$, independent of $\mathbf{X}$. To estimate $\mathbf{\theta}$ relative to quadratic loss function $(\hat{\mathbf{\theta}} - \mathbf{\theta})'\Sigma^{-1}(\hat{\mathbf{\theta}} - \mathbf{\theta})$, we obtain a family of minimax estimators $\mathbf{\delta}(\mathbf{X}, \mathbf{A})$…

存在缺失数据时均值差的估计方法AI 解读

The maximum likelihood estimate of the difference of the means is obtained in sampling from a bivariate normal distribution with unknown variances and co-variance when some of the observations on one of the variables are missing. This estimate is compared to several others by using the mean square error criterion. It is found that, when there are a moderate number of complete pairs of observations, the maximum likelihood estimate has the smallest mean square error for most…