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混合回归估计量协方差矩阵的无偏估计AI 解读

This article derives an unbiased estimator of the covariance matrix of the “mixed regression” estimator suggested by Theil and Goldberger for combining prior information with the sample information in regression analysis. This derivation facilitates the construction of finite-sample standard errors for the mixed estimators of the individual regression coefficients. Comparisons are made between the unbiased covariance estimator, the conventional consistent estimator based on…

“Box 类”似然比准则的大偏差型近似AI 解读

For a large class of tests related to the multivariate normal distribution a number of approximations to the distribution of the log-likelihood ratio statistic are discussed. Some of the approximations require the use of a small personal computer for their calculation, but this pays off in terms of giving very accurate approximations. Actually, one of the approximations, based on the use of a conjugate distribution, works well for all sample sizes and all significance levels.

分层抽样下正态判别与逻辑回归的最优样本分配AI 解读

For two multivariate normal populations with a common covariance matrix and stratified sampling, we consider two methods of estimation—Fisher's linear discriminant function and logistic regression. Intuition suggests that taking half of the observations from each population is a reasonable design choice. Based on minimizing the expected error regret, asymptotic optimal sample allocations are found. The results indicate that the differences in the expected error regret for…

平滑拟合优度检验：分位数函数方法AI 解读

A quantile function based analog to Neyman's smooth tests for goodness-of-fit hypotheses is developed. These procedures possess asymptotic and small-sample power properties similar to those for smooth tests. They are, however, computationally simple, applicable to both complete and Type II censored data, and easily focused in the direction of any specific set of alternatives. These results are used to develop a new test for exponentiality. Only location/scale null hypotheses…

多维参数空间中的稳健贝叶斯分析方法AI 解读

In some multiparameter Bayesian problems the prior is more naturally described as a joint density for all of the parameters and in others it is more naturally described as a product of marginal and conditional densities. Although ordinary quantile, ε-contamination, and density-ratio classes of priors may be sensible choices for robust Bayesian analyses in the former case, they may be less satisfactory in the latter. This article shows how to construct product classes of…

通过可变形模板进行结构图像复原AI 解读

Prior knowledge on the space of possible images is given in the form of a function or template in some domain. The set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself. A prior Gaussian distribution is given on the set of continuous mappings. The observed image is assumed to be a degradation of the true image with additive noise. Given the observed image, a posterior distribution is then…

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利用医疗事故数据预测索赔频率：含随机效应的泊松过程模型AI 解读

I use the Florida state data base (1975–1987) of settled malpractice claims to develop Poisson process models for the frequency of claims filed against individual physicians. These models incorporate random effects and covariates that represent physician attributes and are natural generalizations of the negative binomial model that is typically used to study claims frequency. I predict claims frequencies during 1981–1982 using models that are selected and estimated from…

改进小区域人口估计程序的评价AI 解读

"We provide and illustrate methods for evaluating across-the-board ratio estimation and synthetic estimation, two techniques that might be used for improving population estimates for small areas. The methods emphasize determination of a break-even accuracy of knowledge concerning externally obtained population totals, which marks the point at which improvement occurs." The techniques are illustrated using 1980 U.S. census data.

统计推断：从似然到显著性AI 解读

The concepts of likelihood and significance were defined and initially developed by R. A. Fisher, but followed almost separate and distinct routes. We suggest that a central function of statistical inference is in fact the conversion of the first, likelihood, into the second, significance: a linking of the Fisher concepts. A first-order asymptotic route for this is incorporated into most statistical packages. It uses the standardized maximum likelihood estimate, the…

广义线性模型均值函数的失拟检验AI 解读

A supremum-type statistic, based on partial sums of residuals, is proposed to test the validity of the mean function of the response variable in a generalized linear model. The proposed test does not need a partition of the space of covariates to handle the case of nonreplication. The new test is consistent against the alternative, under which the deterministic part of the model is not the one specified in the null hypothesis. The asymptotic null distribution of the test…

多变量与重复测量设计中秩检验的统一方法AI 解读

A unified approach to asymptotic rank tests is presented for a wide class of univariate and multivariate models, including repeated measures designs without compound symmetry. The models are assumed to be balanced and complete with more than one replication per cell. The proposed rank tests are constructed by ranking all of the observations together regardless of row, column, or component membership. This method of ranking offers increased power over the method of…

贝叶斯统计中的敏感性：先验与似然AI 解读

One paradigm for sensitivity analyses in Bayesian statistics is to specify Γ, a reasonable class of priors, and to compute the corresponding class of posterior inferences. The class Γ is chosen to represent uncertainty about the prior. There is often additional uncertainty, however, about the family of sampling distributions. This article introduces a method for computing ranges of posterior expectations over reasonable classes of sampling distributions that lie “close to” a…

平衡多变量方差分量模型中协方差矩阵的最小二乘估计AI 解读

The problem of estimating covariance matrices in balanced multivariate variance components models is discussed. As with univariate models, it is possible for the traditional estimators, based on differences of the mean square matrices, to produce estimates that are outside the parameter space. In fact, in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite (nnd). In this article we develop an iterative…

密度估计中的数据变换AI 解读

For the density estimation problem the global window width kernel density estimator does not perform well when the underlying density has features that require different amounts of smoothing at different locations. In this article we propose to transform the data with the intention that a global window width is more appropriate for the density of the transformed data. The density estimate of the original data is the “back-transform” by change of variables of the global…

价格与促销弹性的收缩估计：似乎不相关方程AI 解读

Consider the problem where a retailer or manufacturer wants to estimate product price and promotional elasticities based on supermarket scanner data. Classical linear modeling suffers from the following aggregation dilemma. Price and promotional elasticities appear to vary considerably among chains and brands so that one overall model is too restrictive. Alternatively, the use of a different model for each chain and brand leads to noisy and often nonsensical estimates of…

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摘要暂缺

摘要暂缺

摘要暂缺

分层抽样下正态判别与Logistic回归的最优样本配置AI 解读

For two multivariate normal populations with a common covariance matrix and stratified sampling, we consider two methods of estimation—Fisher's linear discriminant function and logistic regression. Intuition suggests that taking half of the observations from each population is a reasonable design choice. Based on minimizing the expected error regret, asymptotic optimal sample allocations are found. The results indicate that the differences in the expected error regret for…

平衡多元方差分量模型中协方差矩阵的最小二乘估计AI 解读

The problem of estimating covariance matrices in balanced multivariate variance components models is discussed. As with univariate models, it is possible for the traditional estimators, based on differences of the mean square matrices, to produce estimates that are outside the parameter space. In fact, in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite (nnd). In this article we develop an iterative…