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未知协方差与任意二次损失下正态均值向量的极小极大估计AI 解读

Let $X$ be an observation from a $p$-variate normal distribution $(p \geqq 3)$ with mean vector $\theta$ and unknown positive definite covariance matrix $\not\Sigma$. It is desired to estimate $\theta$ under the quadratic loss $L(\delta, \theta, \not\Sigma) = (\delta - \theta)^tQ(\delta - \theta)/\operatorname{tr} (Q\not\Sigma)$, where $Q$ is a known positive definite matrix. Estimators of the following form are considered: $\delta^c(X, W) = (I - c\alpha Q^{-1}W^{-1}/(X^tW^{-1}X))X,$…

未知方差下独立正态均值估计问题的合并AI 解读

Let $X = (X_1, \cdots, X_p)^t$ be a $p$-variate normal random vector with unknown mean $\theta = (\theta_1, \cdots, \theta_p)^t$ and unknown positive definite diagonal covariance matrix $A$. Assume that estimates $V_i$ of the variances $A_i$ are available, and that $V_i/A_i$ is $\chi^2_{n_i}$. Assume also that all $X_i$ and $V_i$ are independent. It is desired to estimate $\theta$ under the quadratic loss $\lbrack\sum^p_{i=1} q_i(\delta_i - \theta_i)^2\rbrack/\lbrack\sum^p_{i=1} q_i A_i\rbrack,\quad\text{where} q_i > 0, i = 1, \cdots, p.$…

消除位置向量 Stein 型估计量的奇点AI 解读

Summary In estimating a multivariate location vector in three or more dimensions, it is well known that Stein-type estimators can offer considerable improvement in risk over the best invariant estimator. A common problem arising in the use of such estimators is that simple versions often have a singularity at zero. Methods of eliminating such singularities are discussed in this paper. The resulting estimators are usually considerably better than the uncorrected versions, and…

多元正态分布均值的极小极大估计量AI 解读

An extension of Strawderman's results yields minimax admissible estimates for the mean of a $p$-variate normal distribution where the known nonsingular covariance matrix is not necessarily the identity and $p > 2$. Minimax estimators for the case where the covariance matrix is unknown are also given.

T. A. Yancey, G. G. Judge, M. E. Bock, Wallace's Weak Mean Square Error Criterion for Testing Linear Restrictions in Regression: A Tighter Bound, Econometrica, Vol. 41, No. 6 (Nov., 1973), pp. 1203-1206

回归中预检验估计量的统计后果AI 解读

This study is concerned with deriving the properties of the preliminary test estimator for the general linear normal regression model, ascertaining the characteristics of the risk functions over the parameter space, and determining the conditions necessary for the risk of this estimator to exceed or be less than the conventional one under squared error loss. A test procedure and the problem of choosing an optimal level of significance for the test are discussed. Some…

Theil 混合回归估计量的若干有限样本结果AI 解读

Finite sample properties of Theil's mixed regression estimator and test statistic for checking the compatibility of prior and sample information, are studied via Monte Carlo sampling experiments.

Theil 混合回归估计量的若干有限样本结果AI 解读

Finite sample properties of Theil's mixed regression estimator and test statistic for checking the compatibility of prior and sample information, are studied via Monte Carlo sampling experiments.