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单参数情形下最大似然估计与后验均值的比较AI 解读

Consider estimation of a scalar parameter θ of a distribution on the basis of a random sample of size n. Possible estimators include the maximum likelihood estimator, n , and the posterior mean with respect to some prior distribution, n . In this article n and n are compared by considering a large-sample version of the Pitman nearness criterion; conditions are given under which n is preferable to n in this sense. Several examples are provided that show that comparisons of n…

回归模型整体与局部拟合诊断AI 解读

We concern ourselves with diagnostics for checking the overall and local goodness of fit of a model s(x) used in the regression of Y on x ∈ U = [0, 1] d . The model for s(x) is a functional form that depends on a finite number of unknown parameters. Two statistics, Λ and Λ w , are proposed that measure the level of agreement between the model fit to the data and the nonparametric kernel estimator on m preselected points in U. Conditions are given under which Λ and λ w , are…

贝叶斯与非贝叶斯区间估计之间的关系AI 解读

SUMMARY Let Y 1, ..., Y n denote independent observations each distributed according to a density depending on a scalar parameter θ. Suppose that we are interested in constructing an interval estimate for 0. One approach is to construct a confidence region with a specified coverage probability based on the likelihood ratio test statistic. Another approach is to construct a highest posterior density region with a specified posterior probability. The goal of this paper is to…

无限维参数空间中的最大似然估计AI 解读

An approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions. In this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter. We provide conditions under which the rate of convergence can be established. This rate is essentially governed by the size of the space of score functions as measured by an entropy index. We also show that, for a large class of…

基于似然的显著性检验的条件性质AI 解读

This paper considers the conditional properties of the unconditional significance tests based on standardized versions of the maximum likelihood estimate and the score statistic for the case of a simple null hypothesis and a one-parameter model. The properties of the tests are assessed by considering the conditional level of the test given the observed value of a statistic that is locally ancillary near the null model. It is shown that for the test based on the maximum…

基于似然的显著性检验的条件性质AI 解读

This paper considers the conditional properties of the unconditional significance tests based on standardized versions of the maximum likelihood estimate and the score statistic for the case of a simple null hypothesis and a one-parameter model. The properties of the tests are assessed by considering the conditional level of the test given the observed value of a statistic that is locally ancillary near the null model. It is shown that for the test based on the maximum…