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位置线性判别函数的渐近分布AI 解读

SUMMARY The location linear discriminant function forms the basis of the optimal Bayes classification rule when the data contain both binary and continuous variables (Krzanowski, 1975). When the unknown parameters are replaced by their sample estimates, the resulting “estimative” rule has an exact distribution which is too complicated for numerical use. We present here an asymptotic expansion of this distribution and study its performance under various assumptions about the…

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多元泊松均值估计及相关问题的完全类定理AI 解读

Basic decision theory for discrete random variables of the multivariate geometric (power series) type is developed. Some properties of Bayes estimators that carry over in the limit to admissible estimators are obtained. A stepwise generalized Bayes representation of admissible estimators is developed with estimation of the mean of a multivariate Poisson random variable in mind. The development carries over to estimation of the mean of a multivariate negative Binomial random…

稳健贝叶斯决策程序：数据分布中的严重误差AI 解读

We consider a standard Bayes decision situation except that with small probability the data may be irrelevant to the parameter of interest (i.e. the experiment is "biased"). The minimax solution under quite general assumptions is described and discussed.

贝叶斯集合估计与可容许集合估计AI 解读

We consider the problem of set estimation of a parameter θ based on an observation X, with the goal of simultaneous control of the noncoverage probability and expected size of the estimating set. Several notions of being Bayes for set estimates are studied, and their relationship to a natural notion of admissibility for confidence procedures is investigated.

估计正参数乘积的样本分配方案AI 解读

Suppose that for i = 1, …, I, a random variable whose distribution depends on parameter μ i , > 0 is observable from population i. The problem is to estimate θ = IIμ i , using a Bayesian approach with squared error estimation loss in θ and allowing sequential allocation. That is, k observations may be taken one at a time and the decision to take an observation from population i may depend on past observations from all populations. For estimating θ, the best nonrandom…

相互依赖专家的多变量概率评估AI 解读

When two or more information sources (“experts”) provide a decision maker with information on two or more random variables, the decision maker using Bayes's rule has an opportunity to (a) update a prior about the random variables and (b) calibrate the experts. (Calibration is the process of adjusting the decision maker's likelihood about the experts' assessments.) This article presents a model for this two-way process and specializes to the case in which the experts'…

聚类分析中正确分配率的估计AI 解读

A sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations. The mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership. Estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the…

相关专家的多重概率评估AI 解读

When two or more information sources (“experts”) provide a decision maker with information on two or more random variables, the decision maker using Bayes's rule has an opportunity to (a) update a prior about the random variables and (b) calibrate the experts. (Calibration is the process of adjusting the decision maker's likelihood about the experts' assessments.) This article presents a model for this two-way process and specializes to the case in which the experts'…

聚类分析中正确分配率的估计AI 解读

A sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations. The mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership. Estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the…

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集体诉讼中的损害金额估计AI 解读

In a class action litigation, actual damages are not known exactly and must be estimated. Various estimators are proposed and assessed by using a model that identifies possible sources of error. Estimators that have been used in practice are shown to be seriously biased. An empirical Bayes estimator and an empirical minimal mean squared error estimator are found to be more satisfactory methods for estimating damages.

连续单参数指数族经验贝叶斯检验的渐近行为AI 解读

Several authors have proposed empirical Bayes tests (EBT) for the continuous one-parameter exponential family for the case that the prior distribution is completely unspecified. They investigated the convergence rate of the (unconditional) Bayes risk, and gave upper bounds for this convergence rate. In this paper it is proposed to study the convergence of the conditional Bayes risk. A method is presented which makes it possible to derive the exact convergence rate of the…

多元 Poisson 均值的全部可容许线性估计量AI 解读

Admissible linear estimators $Mx + \gamma$ must be pointwise limits of Bayes estimators. Using properties of Bayes estimators preserved by taking limits, the structure of $M$ and $\gamma$ can be determined. Among $M, \gamma$ with this structure, a necessary and sufficient condition for admissibility is obtained. This condition is applied to the case of linear (mixture) models. It is shown that only the most trivial such models admit linear estimators of full rank which are…

分布变化的最优检测AI 解读

Suppose one is able to observe sequentially a series of independent observations $X_1, X_2, \cdots$ such that $X_1, X_2, \cdots, X_{\nu-1}$ are iid distributed according to a known distribution $F_0$ and $X_\nu, X_{\nu+1}, \cdots$ are iid distributed according to a known distribution $F_1$. Assume that $\nu$ is unknown and the problem is to raise an alarm as soon as possible after the distribution changes from $F_0$ to $F_1$. Formally, the problem is to find a stopping rule $N$…

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二项数据的贝叶斯方法及其在无应答问题中的应用AI 解读

In this article, Bayesian estimation methods for several binomial probabilities are studied by using a mixture of a product of beta prior distributions. Approximations to the posterior means and credible regions are derived. The results obtained are applied to a sample survey problem in which there is significant nonresponse.

现代基础统计学AI 解读

Preface Chapter 1: Introduction 1.1 The Growth of Modern Statistics 1.2 Sources of Statistical Data 1.3 The Nature of Statistical Data Chapter 2: Summarizing Data: Listing and Grouping 2.1 Listing Numerical Data 2.2 Stem-and-Leaf Displays 2.3 Frequency Distribution 2.4 Graphical Presentations 2.5 Summarizing Two-Variable Data Chapter 3: Summarizing Data: Measures of Location 3.1 Population and Samples 3.2 The Mean 3.3 The Weighted Mean 3.4 The Median 3.5 Other Fractiles 3.6…

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