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插补调查数据的方差估计AI 解读

Unit nonresponse and item nonresponse both occur frequently in surveys. Unit nonresponse is customarily handled by weighting adjustment, whereas item nonresponse is usually treated by some form of imputation. In particular, deterministic or stochastic imputation is often used to assign values for missing item responses. We provide an account of some recent work on jackknife variance estimation based on adjusted imputed values, using only a single imputation and hence a…

十八余年后的多重插补AI 解读

Multiple imputation was designed to handle the problem of missing data in public-use data bases where the data-base constructor and the ultimate user are distinct entities. The objective is valid frequency inference for ultimate users who in general have access only to complete-data software and possess limited knowledge of specific reasons and models for nonresponse. For this situation and objective, I believe that multiple imputation by the data-base constructor is the…

马尔可夫链蒙特卡洛收敛诊断：比较综述AI 解读

A critical issue for users of Markov chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but to date has yielded relatively little of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic…

多元分布的洛伦兹 zonoidAI 解读

The article extends the usual Lorenz curve and Lorenz order of univariate distributions to the multivariate case. For a given probability distribution in nonnegative d space, d ≥ 1, we define and investigate the Lorenz zonoid and the Lorenz surface, which are sets in (d + 1) space. The surface equals the usual Lorenz curve when d = 1. Included is the definition of the Lorenz surface of a finite number of vectors that may be interpreted as the endowments of economic units in…

多元数据分位数的几何定义AI 解读

An extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered. The approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles, both of which have been extensively studied in the literature. These geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other L estimates of…

利用有偏样本估计迟发性疾病发病率AI 解读

Consistent estimators are derived for the age-specific and lifetime incidence rates of late-onset diseases from censored, biased samples, using a discrete time model and a traditional assumption for size-biased sampling. The estimators are alternatives to the so-called index case estimators often used by epidemiologists under similar circumstances. The asymptotic normality of the proposed estimators is established and an adaptation of Greenwood's formula is given for…

分层有限总体比例的精确推断AI 解读

Auditors and others often encounter finite populations with a dichotomous characteristic from which they draw stratified samples. In auditing the dichotomy arises when a population item is classified as either in error or in compliance with some rule or regulation. Usually the proportion of errors is small. The auditing objective may require calculation of a p value for the sample outcome relative to a hypothesis, or a confidence bound for the proportion or total number of…

泊松分布与二项分布的似然比检验AI 解读

The estimation of N in the binomial B(N, p) distribution is a considerably harder problem than the estimation of p. We approach it as a “boundary value” estimation and testing problem, where the boundary N = ∞ corresponds to a Poisson distribution for the data, whereas N < ∞ corresponds to a binomial distribution. The asymptotic distribution of the deviance statistic for testing the hypothesis that the true value of N is infinite is shown to be a 50–50 mixture between a…

似然函数与似然原则的推广AI 解读

The parametric likelihood and likelihood principle (LP) play a central role in parametric methodology and in the foundations of statistics. The main purpose of this article is to extend the concepts of likelihood and LP to general inferential aims and models covering, for example, prediction and empirical Bayes models. The likelihood function is the joint distribution of the data and the unobserved variables of inferential interest, considered as a function of the parameters…

贝叶斯序贯两阶段抽样AI 解读

We propose a sequential two-phase sample design to accommodate applications where conventional two-phase sampling cannot be used. First, we derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then we compare our procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a…

推断对先验边际分布的局部敏感性AI 解读

The sensitivity of posterior expectations to perturbations of prior marginals is investigated, using a local method. This approach is particularly well suited to high-dimensional parameter spaces. Qualitative and quantitative results are obtained regarding the propagation of sensitivity in multiparameter settings. More specifically, a posterior expectation is treated as a functional of the prior marginal. The derivative of this functional is evaluated at the nominal prior…

方差分量模型的贝叶斯方法AI 解读

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the…

如何成为更好的贝叶斯统计学家AI 解读

Consider an experiment yielding an observable random quantity X whose distribution is indexed by a real parameter ø. Suppose that a statistician is prepared to execute a Bayes procedure in estimating ø and has quantified available prior information about ø in his chosen prior distribution G. Suppose that before this estimation process is completed, the statistician becomes aware of the outcome Y of a “similar” experiment. In this article we investigate the questions of…

异方差线性模型的秩方法分析AI 解读

Heteroscedasticity often causes problems in the analysis of linear models. Frequently for such cases, scale is a function of the response. Here, for such models, a methodology is presented based on well-known rank-based procedures. The procedure is iterative. Using the residuals from an initial R estimate of the regression coefficients, scale is estimated by inverting a linear rank test for scale. This in turn leads to a weighted R estimate of the regression coefficients and…

两样本分位数比较函数及其诊断标志物应用AI 解读

In this article a control percentile test, a chi-squared test, and a Kolmogorov-type test are proposed for comparing two distributions from incomplete survival data. These tests are obtained by examining a vertical shift comparison function at a single point, a finite number of points, and an entire set of points on an interval. The proposed methods also have applications in receiver operating characteristic (ROC) analysis, which has been widely used in such diverse fields…

基于小波阈值与 Neyman 截断的显著性检验AI 解读

Traditional nonparametric tests, such as the Kolmogorov—Smirnov test and the Cramér—Von Mises test, are based on the empirical distribution functions. Although these tests possess root-n consistency, they effectively use only information contained in the low frequencies. This leads to low power in detecting fine features such as sharp and short aberrants as well as global features such as high-frequency alternations. The drawback can be repaired via smoothing-based test…

Bootstrap 模型选择AI 解读

In a regression problem, typically there are p explanatory variables possibly related to a response variable, and we wish to select a subset of the p explanatory variables to fit a model between these variables and the response. A bootstrap variable/model selection procedure is to select the subset of variables by minimizing bootstrap estimates of the prediction error, where the bootstrap estimates are constructed based on a data set of size n. Although the bootstrap…

基于平滑因子的偏最小二乘回归AI 解读

In this article we present a modification of partial least squares regression to account for inherent nonexchangeabilities of the columns of the design matrix. In chemometrics applications it is common to write the matrix as a bilinear form of latent variables and loadings. These loadings are often interpreted as sampled values of functions; hence they should exhibit a degree of smoothness. Our method forces the partial least squares factors to be smooth, by using a…

基于受扰直方图数据的间接密度估计带宽选择AI 解读

Motivated by a number of practical applications, we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts. Due to variability in the process of correction, the histogram cannot be modeled in terms of simple scaled Poisson statistics. This departure necessitates the development of a new methodology for bandwidth selection. A variant of the method of unbiased risk…

合并似然的经验贝叶斯方法AI 解读

Suppose that several independent experiments are observed, each one yielding a likelihood L k (θ k ) for a real-valued parameter of interest θ k . For example, θ k might be the log-odds ratio for a 2 × 2 table relating to the kth population in a series of medical experiments. This article concerns the following empirical Bayes question: How can we combine all of the likelihoods L k to get an interval estimate for any one of the θ k 's, say θ1? The results are presented in…

插补调查数据分析的替代范式AI 解读

Rubin has offered multiple imputation as a general approach to inference from survey data sets with missing values filled in through imputation. In many situations the multiple imputation variance estimator is consistent. In turn, this observation has lent support to a number of complex applications. In fact, however, the multiple imputation variance estimator is inconsistent under some simple conditions. This article extends previous work of Rao and Shao and of Fay directed…

使用工具变量识别因果效应AI 解读

We outline a framework for causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment effects. We…

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