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组合响应数据的统计建模AI 解读

There is a rich literature for modeling binary and polychotomous responses. However, existing methods are inadequate for handling combinatorial responses, where each response is an integer array under additional constraints. Such data are increasingly common in modern applications, such as surveys collected under skip logic, event propagation on a network, and observed matching in ecology. Ignoring the combinatorial structure leads to biased estimation and prediction. The…

复杂调查数据的贝叶斯经验似然推断AI 解读

Summary We propose a Bayesian empirical likelihood approach to survey data analysis on a vector of finite population parameters defined through estimating equations. Our method allows overidentified estimating equation systems and is applicable to both smooth and non-differentiable estimating functions. Our proposed Bayesian estimator is design consistent for general sampling designs and the Bayesian credible intervals are calibrated in the sense of having asymptotically…

高维贝叶斯有向无环图模型的后验图选择与估计一致性AI 解读

Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are a popular class of models used for this purpose. Gaussian DAG models introduce sparsity in the Cholesky factor of the inverse covariance matrix, and the sparsity pattern in turn corresponds to specific conditional independence assumptions on the underlying variables. A variety of priors have been…

小区域估计中采用全局—局部收缩先验建模随机效应AI 解读

Small area estimation is becoming increasingly popular for survey statisticians. One very important program is Small Area Income and Poverty Estimation undertaken by the United States Bureau of the Census, which aims at providing estimates related to income and poverty based on American Community Survey data at the state level and even at lower levels of geography. This article introduces global–local (GL) shrinkage priors for random effects in small area estimation to…

小区域估计的经验似然方法AI 解读

Abstract Current methodologies in small area estimation are mostly either parametric or heavily dependent on the assumed linearity of the estimators of the small area means. We discuss an alternative empirical likelihood-based Bayesian approach, which neither requires a parametric likelihood nor assumes linearity of the estimators, and can handle both discrete and continuous data in a unified manner. Empirical likelihoods for both area- and unit-level models are introduced.…

高维小样本分类器相对表现的理论度量AI 解读

Summary We suggest a technique, related to the concept of ‘detection boundary’ that was developed by Ingster and by Donoho and Jin, for comparing the theoretical performance of classifiers constructed from small training samples of very large vectors. The resulting ‘classification boundaries’ are obtained for a variety of distance-based methods, including the support vector machine, distance-weighted discrimination and kth-nearest-neighbour classifiers, for thresholded forms…

通过预测相对熵遗憾构造非主观先验AI 解读

We explore the construction of nonsubjective prior distributions in Bayesian statistics via a posterior predictive relative entropy regret criterion. We carry out a minimax analysis based on a derived asymptotic predictive loss function and show that this approach to prior construction has a number of attractive features. The approach here differs from previous work that uses either prior or posterior relative entropy regret in that we consider predictive performance in…

暴露缺失时匹配病例对照研究的半参数贝叶斯分析AI 解读

This article considers Bayesian analysis of matched case-control problems when one of the covariates is partially missing. Within the likelihood context, the standard approach to this problem is to posit a fully parametric model among the controls for the partially missing covariate as a function of the covariates in the model and the variables making up the strata. Sometimes the strata effects are ignored at this stage. Our approach differs not only in that it is Bayesian,…

利用基因表达数据进行肿瘤的贝叶斯分类AI 解读

Summary Precise classification of tumours is critical for the diagnosis and treatment of cancer. Diagnostic pathology has traditionally relied on macroscopic and microscopic histology and tumour morphology as the basis for the classification of tumours. Current classification frameworks, however, cannot discriminate between tumours with similar histopathologic features, which vary in clinical course and in response to treatment. In recent years, there has been a move towards…

具有近似频率学有效性的贝叶斯预测AI 解读

We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability. This is done considering both posterior quantiles and highest predictive density regions with reference to a future observation. The resulting priors are shown to be invariant under reparameterization. The role of Jeffreys’ prior in this regard is also investigated. It is further shown that, for any…

用于小区域估计的广义线性模型AI 解读

Bayesian methods have been used quite extensively in recent years for solving small-area estimation problems. Particularly effective in this regard has been the hierarchical or empirical Bayes approach, which is especially suitable for a systematic connection of local areas through models. However, the development to date has mainly concentrated on continuous-valued variates. Often the survey data are discrete or categorical, so that hierarchical or empirical Bayes…

四人家庭收入中位数估计：贝叶斯时间序列方法AI 解读

This article develops a general methodology for small domain estimation based on data from repeated surveys. The results are directly applied to the estimation of median income of four-person families for the 50 states and the District of Columbia. These estimates are needed by the U.S. Department of Health and Human Services (HHS) to formulate its energy assistance program for low income families. The U.S. Bureau of the Census, by an informal agreement, has provided such…

关于无信息先验的若干讨论AI 解读

This article focuses primarily on a comparison between the reference priors of Berger and Bernardo and the reverse reference priors suggested by J. K. Ghosh. Sufficient conditions are given that provide agreement between the two classes of priors. Several examples are given showing the agreement or disagreement between the two. In addition, these priors are compared under a criterion that requires the frequentist coverage probability of the posterior region of a real-valued…

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约束贝叶斯估计及其应用AI 解读

Bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems. Often, however, the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters. This is for example the situation in subgroup analysis, where the problem is not only to estimate the different components of a parameter vector, but also to identify the parameters…

线性模型中的贝叶斯预测：小区域估计应用AI 解读

This paper introduces a hierarchical Bayes (HB) approach for prediction in general mixed linear models. The results find application in small area estimation. Our model unifies and extends a number of models previously considered in this area. Computational formulas for obtaining the Bayes predictors and their standard errors are given in the general case. The methods are applied to two actual data sets. Also, in a special case, the HB predictors are shown to possess some…

中位数无偏性与Pitman接近性AI 解读

Under certain conditions, a median unbiased estimator of a parameter is shown to be the Pitman-closest estimator within a certain class of estimators. For location, scale, or location-scale families of distributions, the class of equivariant estimators possesses some desirable properties; the median-unbiasedness of equivariant estimators is explored in the characterization of the Pitman closeness property. Illustrative examples bear fruitful implications of this…

熵损失下多个泊松均值的同时估计AI 解读

This paper characterizes admissible linear estimators of multiple Poisson parameters under entropy loss. Estimators dominating some of the standard estimators are given. Further, hierarchical Bayes estimators are generated and conditions under which they dominate the standard estimators are also given. Monte Carlo simulations are undertaken to indicate the extent of the risk dominance.

摘要暂缺

分层样本均值的稳健经验贝叶斯估计AI 解读

This article considers simultaneous estimation of means from several strata, where each stratum contains a finite number of elements. For example, quite often estimates of annual incomes, unemployment rates, and so forth must be made simultaneously for many areas. Our results find application in small area estimation where very few samples are available from an individual area, and an estimate of a certain area mean or simultaneous estimates of several area means can be…

序贯收缩估计AI 解读

The paper develops a class of James-Stein estimators that dominates the sample mean under sequential sampling schemes of Ghosh, Sinha and Mukhopadhyay (1976). Asymptotic risk expansions of the sample mean and James-Stein estimators are provided up to the second-order term. Also, a Monte Carlo study is undertaken to compare the risks of these estimators.

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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.

关于样本中位数自助法的一则说明AI 解读

Efron (1979, 1982), in his treatment of the bootstrap, discusses its use for estimation of the asymptotic variance of the sample median, in the sampling situation of independent and identically distributed random variables with common distribution function $F$ having a positive derivative continuous in a neighborhood of the true median $\mu$. The natural conjecture that the bootstrap variance estimator converges almost surely to the asymptotic variance is shown by an example…