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有限总体总量线性插值估计量的可容许性AI 解读

Consider the problem of estimating the total of some finite population. Suppose the labels attached to the units of the population are such that members of the population whose labels are close together are more alike than units whose labels are far apart. For such a population a sensible estimator of the population total is one that interpolates linearly between successive members of the sample. The admissibility of this estimator will be demonstrated. The related interval…

有限总体抽样区间估计的无信息贝叶斯方法AI 解读

A noninformative Bayesian approach to interval estimation in finite population sampling is discussed. Given the sample, this method introduces the Polya distribution as a pseudo posterior distribution over the unobserved members of the population. In many cases this distribution yields interval estimates similar to those of standard frequentist theory. In addition, it can be used in situations where the standard methods are difficult to apply, for example, in producing an…

有限总体抽样区间估计的无信息贝叶斯方法AI 解读

A noninformative Bayesian approach to interval estimation in finite population sampling is discussed. Given the sample, this method introduces the Polya distribution as a pseudo posterior distribution over the unobserved members of the population. In many cases this distribution yields interval estimates similar to those of standard frequentist theory. In addition, it can be used in situations where the standard methods are difficult to apply, for example, in producing an…

摘要暂缺

若干可容许的非参数估计量及相关有限总体抽样估计量AI 解读

Given a random sample from an unknown distribution $F,$ which is assumed to belong to some nonparametric family of distributions, consider the problem of estimating $\gamma(F),$ some function of $F.$ When the loss function is squared error, admissible estimators are exhibited for a large class of $\gamma$'s. A relationship between these estimators and similar ones in finite population sampling is demonstrated.

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.

随机效应模型的一种新贝叶斯分析AI 解读

SUMMARY For a typical random effects model in the one way analysis of variance a new Bayesian analysis is offered. An exchangeable prior distribution is defined over the parameters. It is suggested that rather than use the usual “F” test one should consider this as an estimation problem. The posterior distribution of a function of the parameters which measures the amount of variation present is found.

利用先验信息估计分层总体总量的可容许估计量AI 解读

We consider the problem of the estimation of the total of a stratified finite population. For two levels of prior knowledge about the stratification, we provide Bayes and pseudo-Bayes estimators that make use of this prior knowledge in sensible ways. We then note that admissibility results can be established for these estimators using the techniques of Meeden and Ghosh (1982, 1983) and indicate some possible natural extensions of the present work.

贝叶斯概率评估者的校准、充分性与支配关系AI 解读

DeGroot and Fienberg (1982a) recently considered various aspects of the problem of evaluating the performance of probability appraisers. After briefly reviewing their notions of calibration and sufficiency we introduce related ideas of semicalibration and domination and consider their relationship to the earlier concepts. We then discuss some simple Bayesian mechanisms for making probability assessments and study their calibration, semicalibration, sufficiency, and…

贝叶斯概率评估的校准、充分性与支配关系AI 解读

DeGroot and Fienberg (1982a) recently considered various aspects of the problem of evaluating the performance of probability appraisers. After briefly reviewing their notions of calibration and sufficiency we introduce related ideas of semicalibration and domination and consider their relationship to the earlier concepts. We then discuss some simple Bayesian mechanisms for making probability assessments and study their calibration, semicalibration, sufficiency, and…

无偏性作为贝叶斯性的对偶AI 解读

In this note we define the notion of unbiasedness for a decision function for an arbitrary loss function. This is a generalization of Lehmann's (1951) definition. We show that this notion of unbiasedness is a dual to the notion of being Bayes; that is, if the role of the random variable and the parameter is interchanged, then unbiasedness is equivalent to being Bayes and vice versa. Some consequences of this fact are discussed.

摘要暂缺

纳入复杂度成本时预检验估计量的可容许性AI 解读

Consider the problem of estimating the mean by using a random sample from a normal population. Let denote the sample mean and consider the estimator that assumes the value zero when and the value when . This is called a preliminary test estimator. For most of the usual loss functions it is inadmissible. In this article we show that for some loss functions, which include a complexity cost, the estimator is admissible. The results are related to Cohen's work on hybrid…

大观测值下后验分布的近似行为AI 解读

Let $X$ be a real valued random variable with a family of possible distributions belonging to a one parameter exponential family with the natural parameter $\theta \in(\underline{\theta}, + \infty)$. Let $g$ be a prior probability density for $\theta$ with unbounded support. Under some additional assumptions it is shown that for large values of $x$ the posterior distribution of $\theta$ given $X = x$ is approximately normally distributed about its mode. If $\delta_g$ denotes…

单参数指数族中线性估计量的可容许性AI 解读

For estimating the mean in the one parameter exponential family with quadratic loss, Karlin (1958) gave sufficient conditions for admissibility of estimators of the form $aX$. Later, Ping (1964) and Gupta (1966) gave sufficient conditions for admissibility of estimators of the form $aX + b$ for the same problem. Zidek (1970) gave sufficient conditions for the admissibility of $X$ for estimating an arbitrary piecewise continuous function of the parameter, say $\gamma(\theta)$,…

利用次序统计量矩集合刻画分布AI 解读

It is known that the set $M = \{\mu_{r,n} : r = 1, 2, \cdots, n; n = 1, 2, 3, \cdots\}$ of expectations of order statistics of samples from a distribution $F$ completely determines $F$ (see, for example, Hoeffding (1953)). In addition Chan (1967), Konheim (1971) and Pollak (1973) have shown that certain subsets of $M$ determine $F$. In this note conditions are derived which are sufficient for a proper subset of $M$ to determine $F$.