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有界非对称损失下线性回归的最优中位数无偏估计AI 解读

This article considers optimal median-unbiased estimation in a linear regression model with the distribution of the errors lying in a subclass of the elliptically symmetric distributions. The generalized least squares (GLS) estimator is shown to be best for any monotone loss function, that is, any loss function that is nondecreasing as the magnitude of underestimation or overestimation increases. This includes bounded asymmetric loss functions. For the same loss functions, a…

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用水调查日记记录分析中的贝叶斯方法应用AI 解读

One of the objectives of a comprehensive domestic water use study conducted in Perth, Western Australia, was the quantification of components of water usage. Each household in a sample of about 3,000 was asked to record all water uses in a specially provided diary for a 2-week period, and the total water usage, both in-house and ex-house, was metered daily during this time. This article describes an application of Bayesian methodology to the estimation of usage for each…

多元岭回归AI 解读

A multivariate linear regression model with q responses as a linear function of p independent variables is considered with a p × q parameter matrix B. The least-squares or normal-theory maximum likelihood estimate of B is deficient in that it takes no account of the ‘across regression’ correlations, and ignores the Stein effect. A remedy was offered by Brown & Zidek (1980) in the form of a multivariate ridge estimator. A richer class of estimators is obtained here by casting…

贝叶斯框架下归类、总体区分与概率确定中的影响观测检测AI 解读

Normal theory separation and allocation problems are discussed from a predictive point of view. Influence statistics are defined and employed to ascertain the impact that particular observations will have on the inferential goals—allocation of future observations, separation between populations, and the determination of probabilities for future cases. Methods are illustrated on a collection of financial data taken from Johnson and Wichern (1982).

Beta–二项模型的贝叶斯估计与预测AI 解读

The beta-binomial distribution, which is generated by a simple mixture model, has been widely applied in the social, physical, and health sciences. Problems of estimation, inference, and prediction have been addressed in the past, but not in a Bayesian framework. This article develops Bayesian procedures for the beta-binomial model and, using a suitable reparameterization, establishes a conjugate-type property for a beta family of priors. The transformed parameters have…

利用递减密度极大似然估计的均匀分布单调经验贝叶斯检验AI 解读

An empirical Bayes test for testing $\vartheta \leq \vartheta_0$ against $\vartheta > \vartheta_0$ for the uniform distribution on $\lbrack 0, \vartheta)$ is discussed. The relation is shown with the estimation of a decreasing density on $\lbrack 0, \infty)$ and a monotone empirical Bayes test is derived based on the least-concave majorant of the empirical distribution function. The asymptotic distribution of the Bayes risk is obtained and some Monte Carlo results are given.

非中心参数估计的完全类定理AI 解读

In statistical decision theory, an important question is to characterize the admissible rules. In this paper, we establish complete class theorems for estimating the noncentrality parameter of noncentral chi-square and noncentral $F$ distributions under squared error loss. Under a minor assumption, any admissible estimator must be a generalized Bayes rule. Using this result, we prove that the positive part of the UMVUE is inadmissible.

列联表独立性的混合 Dirichlet 贝叶斯检验：稳健性与敏感性AI 解读

A mixed-Dirichlet prior was previously used to model the hypotheses of "independence" and "dependence" in contingency tables, thus leading to a Bayesian test for independence. Each Dirichlet has a main hyperparameter $\kappa$ and the mixing is attained by assuming a hyperprior for $\kappa$. This hyperparameter can be regarded as a flattening or shrinking constant. We here review the method, generalize it and check the robustness and sensitivity with respect to variations in…

条件异方差时间序列模型AI 解读

Under the traditional linear time series or regression setting, the conditional variance of one-step-ahead prediction is time invariant. Experience in conjunction with data analysis, however, suggests that the variability of a process might well depend on the available information. This reality has motivated extensive research to relax the constant variance assumption imposed by the traditional linear time series model, and several classes of generalized parametric models…

随机化回答模型的贝叶斯线性估计量AI 解读

Bayes linear estimators provide simple Bayesian methods and require a minimum of prior specification. In this article, Bayes linear estimators are derived for a variety of randomized response models. Randomized response aims to reduce false responses on sensitive questions, at the expense of some loss of information in each observation. In this context, Bayesian methods are attractive because they permit the incorporation of potentially useful prior information. The basic…

通过数据增广计算后验分布AI 解读

The idea of data augmentation arises naturally in missing value problems, as exemplified by the standard ways of filling in missing cells in balanced two-way tables. Thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze. This device is used to great advantage by the EM algorithm (Dempster, Laird, and Rubin 1977) in solving maximum likelihood problems. In situations when the likelihood cannot be approximated closely by…

广义可加模型：若干应用AI 解读

Generalized additive models have the form η(x) = α + σ fj (x j ), where η might be the regression function in a multiple regression or the logistic transformation of the posterior probability Pr(y = 1 | x) in a logistic regression. In fact, these models generalize the whole family of generalized linear models η(x) = β′x, where η(x) = g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions fj (xj )…

三维列联表的贝叶斯对数线性估计AI 解读

This paper presents a Bayesian method to estimate the expected proportions in a three-way contingency table appropriate when prior knowledge about the main, first and second-order interaction effects can be described by a particular kind of exchange ability assumption. The proposed Bayes estimates are calculated by finding those values of the effects which maximize the resulting posterior distribution and can be used to explore the possibility that a nonsaturated submodel,…

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面向第二阶段最佳表现优化的子集选择AI 解读

In the search for the best of n candidates, two-stage procedures of the following type are in common use. In a first stage, weak candidates are removed, and the subset of promising candidates is then further examined. At a second stage, the best of the candidates in the subset is selected. In this article, optimization is not aimed at the parameter with largest value but rather at the best performance of the selected candidates at Stage 2. Under a normal model, a new…

贝叶斯 bootstrap 的大样本研究AI 解读

An asymptotic justification of the Bayesian bootstrap is given. Large-sample Bayesian bootstrap probability intervals for the mean, the variance and bands for the distribution, the smoothed density and smoothed rate function are also provided.

以可容许性为试金石AI 解读

Consider the problem of estimating simultaneously the means $\theta_i$ of independent normal random variables $x_i$ with unit variance. Under the weighted quadratic loss $L(\theta, a) = \sum_i\lambda_i(\theta_i - a_i)^2$ with positive weights it is well known that: (1) An estimator which is admissible under one set of weights is admissible under all weights. (2) Estimating individual coordinates by proper Bayes estimators results in an admissible estimator. (3) Estimating…

有向图的贝叶斯模型AI 解读

Holland and Leinhardt (1981) proposed a simple exponential model called the p 1 model for analyzing digraphs that arise in studies of networks. A digraph consists of a set of g nodes and a g × g adjacency matrix (Xij ), where Xij = 1 if node i relates to node j and Xij = 0 otherwise. The underlying cell probabilities pij = Pr(Xij = 1) are to be estimated from these dichotomous responses. The p 1 model imposes an additive structure on a log-odds version of the pij . It…

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关于优势比的贝叶斯推断中的最优样本分配AI 解读

The choice of ratio of sample sizes of two groups of binary observations for comparing two proportions is studied using a Bayesian approach. Prior uncertainty about the unknown proportions thus enters the design calculations.

构建线性时间序列模型的候选集合AI 解读

The paper applies selection criteria to order determination in linear time series models in a less mechanical fashion than is often found. This is achieved via posterior odds ratios and by applying concepts of grades of evidence advanced by Jeffreys (1961). It is shown how alternative specifications may be compared and this leads to the development of a practical method for determining a portfolio of different models, each of which may be regarded as reasonable for the data…

再论随机过程的后验渐近正态性AI 解读

SUMMARY The problem of demonstrating the limiting normality of a posterior distribution arising from some stochastic process is revisited. It is shown that certain processes of practical interest are not covered by conditions currently available in the literature. In this paper we present a fairly general set of conditions for asymptotic posterior normality which cover a wide class of problems. The theory is applied to a nonhomogeneous Poisson process and birth process.