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评价层级贝叶斯与经验贝叶斯模型的贝叶斯预测信息准则AI 解读

The problem of evaluating the goodness of the predictive distributions of hierarchical Bayesian and empirical Bayes models is investigated. A Bayesian predictive information criterion is proposed as an estimator of the posterior mean of the expected loglikelihood of the predictive distribution when the specified family of probability distributions does not contain the true distribution. The proposed criterion is developed by correcting the asymptotic bias of the posterior…

利用辅助协变量的加性风险回归AI 解读

We consider the additive hazard model when some of the true covariates are measured only on a randomly selected validation set whereas auxiliary covariates are observed for all study subjects. An updated pseudoscore estimation approach is proposed for the parameters of the additive hazard model. It allows one to fit the model with auxiliary covariates, while leaving the baseline hazard unspecified. Asymptotic properties of the proposed estimators are established, and…

分析区间删失数据的伪似然方法AI 解读

We introduce a method based on a pseudolikelihood ratio for estimating the distribution function of the survival time in a mixed-case interval censoring model. In a mixed-case model, an individual is observed a random number of times, and at each time it is recorded whether an event has happened or not. One seeks to estimate the distribution of time to event. We use a Poisson process as the basis of a likelihood function to construct a pseudolikelihood ratio statistic for…

同质总体规模的植入捕获估计AI 解读

We consider maximum likelihood estimation of the size of a target population to which has been added a known number of planted individuals. The standard equal-catchability model used in mark-recapture is assumed to be applicable to the augmented population. After proving the unimodality of the profile likelihood for the target population size, we obtain both the maximum likelihood estimator of this size and interval estimators based on its asymptotic distribution.

半参数偏正态分布的约束局部似然估计AI 解读

A local likelihood estimator for a nonparametric nuisance function is proposed in the context of semiparametric skew-normal distributions. Constraints imposed on such functions result in a nonparametric estimator with a different target function for maximization from classical local likelihood estimators. The optimal asymptotic semiparametric efficiency bound on parameters of interest is achieved by using this estimator in conjunction with an estimating equation formed by…

利用独立性对数似然对聚类数据进行推断AI 解读

We use the properties of independence estimating equations to adjust the ‘independence’ loglikelihood function in the presence of clustering. The proposed adjustment relies on the robust sandwich estimator of the parameter covariance matrix, which is easily calculated. The methodology competes favourably with established techniques based on independence estimating equations; we provide some insight as to why this is so. The adjustment is applied to examples relating to the…

扩展常规先验以检验线性模型中的一般假设AI 解读

We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objective Bayesian, model-selection perspective. Crucial ingredients for this approach are ‘proper objective priors’ to be used for deriving the Bayes factors. Jeffreys-Zellner-Siow priors have good properties for testing null hypotheses defined by specific values of the parameters in…

响应缺失且协变量存在测量误差的部分线性模型AI 解读

We consider partially linear models of the form Y = X(T)beta + nu(Z) + epsilon when the response variable Y is sometimes missing with missingness probability pi depending on (X, Z), and the covariate X is measured with error, where nu(z) is an unspecified smooth function. The missingness structure is therefore missing not at random, rather than the usual missing at random. We propose a class of semiparametric estimators for the parameter of interest beta, as well as for the…

潜变量问题中的模糊 p 值AI 解读

We consider the problem of testing a statistical hypothesis where the scientifically meaningful test statistic is a function of latent variables. In particular, we consider detection of genetic linkage, where the latent variables are patterns of inheritance at specific genome locations. Introduced by Geyer & Meeden (2005), fuzzy p-values are random variables, described by their probability distributions, that are interpreted as p-values. For latent variable problems, we…

处理或响应变量不可观测时因果效应的图形可识别性判据AI 解读

We consider the problem of using data in studies with an unobserved treatment/response variable in order to evaluate average causal effects, when cause-effect relationships between variables can be described by a directed acyclic graph and the corresponding recursive factorization of a joint distribution. The paper proposes graphical criteria to test whether average causal effects are identifiable even if a treatment/response variable is unobserved. If the answer is…

多元回归条件均值的最优充分降维AI 解读

The aim of this article is to develop optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression. The context is roughly the same as that of a related method by Cook & Setodji (2003), but the new method has several advantages. It is asymptotically optimal in the sense described herein and its test statistic for dimension always has a chi-squared distribution asymptotically under the null hypothesis. Additionally, the optimal method…

缺失响应问题中的经验似然推断及其观察性研究应用AI 解读

Summary The problem of missing response data is ubiquitous in medical and social science studies. In the case of responses that are missing at random (depending on some covariate information), analyses focused only on the complete data may lead to biased results. Various debias methods have been extensively studied in the literature, particularly the weighting method that was motivated by Horvitz and Thompson's estimators. To improve efficiency, Robins, Rotnitzky and Zhao…

平稳空间点过程的最小二乘拟合AI 解读

Summary The K-function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K-function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through…

构建稠密可变形模板估计的统一统计框架AI 解读

Summary The problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge. We provide a careful definition and analysis of a well-defined statistical model based on dense deformable templates for grey level images of deformable objects. We propose a rigorous Bayesian framework for which we prove…

非线性协整型模型中的非参数估计AI 解读

We derive an asymptotic theory of nonparametric estimation for a time series regression model Zt=f(Xt)+Wt, where {Xt} and {Zt} are observed nonstationary processes and {Wt} is an unobserved stationary process. In econometrics, this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results are of wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent Markov chains. This…

非独立同分布观测下后验分布的收敛速度AI 解读

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent, nonidentically distributed observations, Markov processes, stationary Gaussian time series and the white noise model. We…

稳定标记点过程AI 解读

In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson process. Under this assumption, we study the limit behavior of the partial sums of the marked point process {(ti, X(ti))}, where X(t) is a stationary random field and the points ti are generated from an independent Poisson random measure ℕ…

多元失效时间数据的变系数风险模型AI 解读

Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating the unknown coefficient functions. A weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator. The consistency and asymptotic normality of the proposed estimators are established and standard…

识别正交饱和设计中活跃效应的逐步上升同时检验AI 解读

A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects) under the commonly used assumption of effect sparsity. It is shown that each procedure controls the experimentwise error rate at a given α level in the strong sense.

对称分布混合模型的推断AI 解读

This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no additional assumptions other than symmetry are made regarding the parametric form of the component distributions. Because the class of symmetric distributions is so broad, identifiability of parameters is a major issue in these mixtures. We…

In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse regression (SIR). SIR can achieve $\sqrt{n}$ consistency even when each slice contains only two data points. However, SAVE cannot be $\sqrt{n}$ consistent and it even turns out to be not consistent when each slice contains a fixed number of…

流形上的渐近数据分析AI 解读

Given an m-dimensional compact submanifold M of Euclidean space Rs, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general Rs-valued functionals including median location, which is derived from the spatial median. The asymptotic statistical inference for general functionals of distributions on such submanifolds is elaborated. Convergence properties are studied in relation to the behavior of the underlying…

多元独立性 Cramér–von Mises 检验的渐近局部效率AI 解读

Deheuvels [J. Multivariate Anal. 11 (1981) 102–113] and Genest and Rémillard [Test 13 (2004) 335–369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent Cramér–von Mises statistics derived from a Möbius decomposition of the empirical copula process. A result on the large-sample behavior of this process under contiguous sequences of alternatives is used here to give a representation of the limiting…

回归 MM 估计与约束 M 估计的最大偏差函数AI 解读

We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the τ-estimates of regression. In these comparisons, the CM-estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a CM-estimate which has a smaller maximum bias function than a given S-estimate, that is,…