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位置参数推断中的异常值与尾部可信度AI 解读

Heavy-tailed distributions are important for modeling problems in which there may be outlying observations or parameters. Examples of their use are given in O'Hagan (1988). This article develops some general theory, based on the notion of credence, for inference about unknown location parameters in the case of known variances. A density on the real line is defined to have credence c if it is bounded above and below by positive multiples of (1 + x 2)-c/2. For instance, a t…

经验贝叶斯置信区间的构造方法AI 解读

Parametric empirical Bayes (EB) methods of point estimation date to the landmark paper by James and Stein (1961). Interval estimation through parametric empirical Bayes techniques has a somewhat shorter history, which was summarized by Laird and Louis (1987). In the exchangeable case, one obtains a “naive” EB confidence interval by simply taking appropriate percentiles of the estimated posterior distribution of the parameter, where the estimation of the prior parameters…

经验贝叶斯置信区间的构造方法AI 解读

Parametric empirical Bayes (EB) methods of point estimation date to the landmark paper by James and Stein (1961). Interval estimation through parametric empirical Bayes techniques has a somewhat shorter history, which was summarized by Laird and Louis (1987). In the exchangeable case, one obtains a “naive” EB confidence interval by simply taking appropriate percentiles of the estimated posterior distribution of the parameter, where the estimation of the prior parameters…

基于模型的统计学的一般框架AI 解读

This paper presents a general framework for model-based statistics. The framework is based on extended concepts of sufficiency and ancillarity. The fundamental theorem of the new theory exhibits in a single equation the reference distributions for decision theory, model checking, and conditional inference for a general statistical model. The theorem includes the equations upon which Bayesian and frequentist statistics are founded. The general theory also fills two gaps…

摘要暂缺

Marshall–Olkin 指数分布的贝叶斯估计AI 解读

SUMMARY Bayes estimators of the parameters of the Marshall–Olkin exponential distribution are obtained when random samples from series and parallel systems are available. The estimators are with respect to the quadratic loss function, and the prior distribution allows for prior dependence among the components of the parameter vector. Exact and approximate highest posterior density credible ellipsoids for the parameters are also obtained. In contrast with series sampling, the…

This article adapts to the regional level a multicountry technique recently used by Garcia-Ferrer, Highfield, Palm, and Zellner (1987) and extended by Zellner and Hong (1987) to forecast the growth rates in gross national product across nine countries. This forecasting methodology is applied to the regional level by modeling payroll formation in seven Ohio metropolitan areas. We compare the forecasting performance of these procedures with that of a ridge estimator and find…

衡量单个观测对贝叶斯因子的影响AI 解读

In this paper we consider a measure of the effect of single observations on a logarithmic Bayes factor defined via the difference in the logarithms of the Bayes factors conditional first on all the data and then omitting an observation. The measure is related to the conditional predictive ordinate. The form of the measure and examples of its use are presented for a variety of situations, normal samples, linear models, log linear models and the checking of distributional…

一般层级模型中异常值的识别与处理AI 解读

By their nature, hierarchical models involve a considerable number of structural and distributional assumptions; for example, normality and linearity are common assumptions. Considerations of robustness therefore suggest that some form of model elaboration is necessary. However, it is not clear how to achieve this in the already complex setting of hierarchical models whilst maintaining reasonable tractability in the analysis. We provide a comprehensive account of the way in…

通过数据增广计算最高后验密度区域的概率含量与边界AI 解读

This note considers the computation of the content and the boundary of the highest posterior density region in the context of data augmentation. The notion of the highest posterior density region and the data augmentation algorithm are reviewed. The sampling-based approach for calculating the content and the boundary of the highest posterior density region is then presented. The method is illustrated in the context of right-censored regression data.

指数分布第二类删失数据的相对信息损失AI 解读

This paper uses information theory to quantify information loss in Type II censored samples drawn from an exponential distribution. Indexes of information loss for the maximum likelihood estimation and for Bayesian analysis are defined. Properties of the proposed information measures as functions of the sample size, the exponential parameter, and the parameters of the prior distribution are studied. It is shown that the relative loss of information in Type II censoring may…

比率策略的渐近极小极大性AI 解读

The use of simple random sampling together with ratio estimation is of fundamental importance in survey sampling practice. From a theoretical point of view the ratio estimator has been justified by Bayesian methods (Ericson, 1969) and by superpopulation methods (Royall, 1970). But these methods do not yield a rigorous justification of simple random sampling at the same time. We use the minimax principle in an asymptotic version to justify both simple random sampling and…

To study time-dependent characteristics of a population, we may sample the same population at regular intervals. A basic problem is how the sample should be selected at different time periods. Here we consider successive sampling with partial replacement of units on two occasions from a Bayesian point of view. Bayes estimators and optimal designs for such priors will be obtained. In one situation, the whole survey, i.e. the first sample and the second sample, is planned…

非正态线性回归：高维显著性水平的一个例子AI 解读

Analysis of nonnormal linear models leads to an initial conditioning on the standardized residuals, giving an unnormed density on Rk, where k is the number of parameters. To obtain an observed level of significance for a single parameter it is then necessary to calculate a marginal probability, thus requiring integration in k dimensions. In this paper a conditional approach to evaluating the observed level of significance is developed, and an importance sampling technique is…

对称单峰密度及其众数的贝叶斯方法AI 解读

Bayes solutions for i.i.d. sampling from a decreasing density on the half line and for i.i.d. sampling from a symmetric unimodal density with an unknown mode are given. Posterior quantities are obtained as finite sums; Monte Carlo methods based on sampling finite Markov chains are developed for their evaluation.

删失下 Kaplan–Meier 及其他最大似然估计量的可容许性AI 解读

For the nonparametric estimation of a survival function when censoring is present, the Kaplan-Meier estimator is often used. The admissibility of this estimator and other related maximum likelihood estimators is demonstrated. This is done by reducing the problem to one involving just the multinomial distribution and then using the stepwise Bayes technique to prove admissibility.

帕累托数据的贝叶斯估计与预测AI 解读

Data from a classical Pareto distribution are to be used to make inferences about the inequality and precision parameters. In addition, it is desired to predict the behavior of further observations from the distribution. Three typical data configurations are considered (iid and two types of censoring). Dependent conjugate prior analyses are reviewed and are compared with an analysis involving independent priors for the inequality and precision parameters. It is argued that…

方向数据的自助法置信区域AI 解读

Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article differs from that of other authors in that it is based on pivotal statistics. A general pivotal method is introduced that produces a wide variety of confidence regions on general p-dimensional spheres; included are confidence cones and likelihood-based regions.…

贝叶斯边际推断AI 解读

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and…

十年人口普查漏计的经验贝叶斯估计AI 解读

On April 1, 1990, the decennial census for the United States will be conducted by the U.S. Bureau of the Census. By December 31, 1990, the Census Bureau is specified by law to submit state population counts for the purpose of reapportionment of the U.S. House of Representatives, and by March 31, 1991, to submit small-area population counts for the purpose of redistricting. Census counts are used in a variety of other ways: for revenue-sharing formulas between different…

调查抽样的统一理论与策略AI 解读

Part A: Unified Theory of Sampling. Introduction. Principal Notation and Formulation of the Main Problem. Design-Based Estimation. Admissibility and Other Optimality Properties of Sampling Designs. Sufficiency and Related Concepts in Survey Sampling. Sample Survey and General Statistical Model. Further Details on Likelihood and Bayesian Approach. Predictive Approach. Robustness. Concluding Remarks. Appendices: An Optimality Property of the Sample Mean. Alternative Models and…

方向数据的Bootstrap置信区域AI 解读

Methods are proposed for constructing bootstrap confidence regions for the mean direction of a random p-dimensional unit vector X with an arbitrary unimodal distribution on the p sphere. The approach of this article differs from that of other authors in that it is based on pivotal statistics. A general pivotal method is introduced that produces a wide variety of confidence regions on general p-dimensional spheres; included are confidence cones and likelihood-based regions.…

贝叶斯边际推断AI 解读

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and…

利用蒙特卡洛积分进行计量经济模型的贝叶斯推断AI 解读

Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the posterior density. These densities are modified…