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未知方差的异质正态观测之共同均值估计AI 解读

Summary To determine the common mean of heterogeneous normal observations, the Bayes procedures and the invariant maximum likelihood estimators of the weights forming the weighted means statistic are obtained when there are no variance estimates. The Bayes statistic is based on the reference, Geisser–Cornfield prior distribution which makes the posterior (discrete) distribution of the mean to be supported by the observed data with probabilities determined via the geometric…

元分析中异质性方差的估计AI 解读

Summary Several new estimators of the between-study variability in a heterogeneous random effects meta-analysis model are derived. One is the unbiased statistic which is locally optimal for small values of the parameter. Others are Bayes procedures within a class of quadratic statistics for a diffuse prior with different choices of the prior mean. These estimators are compared with the DerSimonian–Laird procedure and the Hedges statistic in particular via the quadratic risk…

实验室间研究中的同时估计与不一致性降低AI 解读

Summary Several procedures that are designed to reduce nonconformity in interlaboratory studies by shrinking data towards a consensus weighted mean are suggested. Some of them are shown to have a smaller quadratic risk than the vector sample means. Shrinkage towards a weighted mean in a random-effects model and a statistic appearing in models which allow for systematic errors are also considered. The results are illustrated by two examples of collaborative studies.

共同均值估计与加权均值统计量AI 解读

Measurements made by several laboratories may exhibit nonnegligible between-laboratory variability, as well as different within-laboratory variances. Also, the number of measurements made at each laboratory often differ. Questions of fundamental importance in the analysis of such data are how to form a best consensus mean, and what uncertainty to attach to this estimate. An estimation equation approach due to Mandel and Paule is often used at the National Institute of…

共同均值估计与加权均值统计量AI 解读

Measurements made by several laboratories may exhibit nonnegligible between-laboratory variability, as well as different within-laboratory variances. Also, the number of measurements made at each laboratory often differ. Questions of fundamental importance in the analysis of such data are how to form a best consensus mean, and what uncertainty to attach to this estimate. An estimation equation approach due to Mandel and Paule is often used at the National Institute of…

分离假设检验与自适应检验统计量的 Bahadur 效率AI 解读

The notion of separability of hypotheses was first introduced by Cox (1961); two families of hypotheses are separate if no distribution in one family can be obtained as a limit of distributions from the other family. For testing separate hypotheses, Cox (1961, 1962) suggested the test based on the comparison of the logarithm of the likelihood ratio with its expected value (or estimate thereof) under each hypothesis. The tests of such hypotheses are required to have high…

用于损失估计的损失函数AI 解读

A class of proper scoring functions which combine the error in a decision problem and the precision of the statistical decision rule is introduced. The Bayesian procedures with respect to these loss functions are pairs formed by the usual Bayes decision and by the expected posterior loss. A necessary and sufficient condition for admissibility under the corresponding risk is given.

二项分布参数估计量的损失估计AI 解读

A loss function is introduced, which combines the estimation error of a statistical procedure with a measure of its accuracy. The properties of this loss function are illustrated by the estimator of a binomial parameter. The choice of a conjugate prior distribution is discussed from this point of view. It is shown that there exists a unique beta prior with a conservatively biased accuracy estimate.

二项参数估计量的损失估计AI 解读

A loss function is introduced, which combines the estimation error of a statistical procedure with a measure of its accuracy. The properties of this loss function are illustrated by the estimator of a binomial parameter. The choice of a conjugate prior distribution is discussed from this point of view. It is shown that there exists a unique beta prior with a conservatively biased accuracy estimate.

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指数分布分位数估计的容许性与极小极大性AI 解读

The estimation problem of the quantiles $\xi + b\sigma$ of an exponential distribution with unknown location-scale parameter $(\xi, \sigma)$ is considered. We establish the admissibility of the traditional (best equivariant) estimator for quadratic loss when $n^{-1} \leq b \leq 1 + n^{-1}$ where $n$ is the sample size. For $b > 1 + n^{-1}$ a class of minimax procedures is found. This class contains generalized Bayes rules and one of them is shown to be admissible within the…

自适应分类程序AI 解读

An explicitly computable, necessary, and sufficient condition for the existence of an adaptive classification procedure is obtained. By definition, an adaptive procedure, which classifies a sample as coming from one of alternative distributions known only up to a finite-valued nuisance parameter, is required to have the same asymptotic behavior of error probability for these families as asymptotically optimal rules for each of the families. We investigate the conditions…

有限取值参数估计的收敛速度：错误概率能有多小？AI 解读

In this paper we investigate the rates of convergence to zero of error probabilities in the estimation problem of a finite-valued parameter. It is shown that if a consistent estimator attains Bahadur's bound for the probability of incorrect decision at some parametric point then the error probability does not tend to zero exponentially fast for some other value of the parameter. We evaluate the minimal possible rate of convergence of this probability at a fixed parametric…

多重决策与假设检验中的自适应程序AI 解读

Necessary and sufficient conditions for the existence of adaptive procedures for identification of one of several probability distributions or for testing a simple hypothesis against a simple alternative are obtained. By definition, adaptive procedures are required to exhibit the same asymptotic behavior for several parametric families as do the optimal (minimax) estimators for each of these families. The proofs are based on a multivariate version of Chernoff's theorem,…

指数分布分位数的估计AI 解读

We consider the problem of estimating a quantile ξ + bσ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator is inadmissible if 0 ≤ b < n-1 or b > 1 + n 1. For b > 1 + n 1 the estimator elsewhere, provides a noticeable improvement over δ0.