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客观贝叶斯、条件推断与有符号平方根似然比统计量AI 解读

Bayesian properties of the signed root likelihood ratio statistic are analysed. Conditions for first-order probability matching are derived by the examination of the Bayesian posterior and frequentist means of this statistic. Second-order matching conditions are shown to arise from matching of the Bayesian posterior and frequentist variances of a mean-adjusted version of the signed root statistic. Conditions for conditional probability matching in ancillary statistic models…

指数族中的客观贝叶斯与条件推断AI 解读

Objective Bayes methodology is considered for conditional frequentist inference about a canonical parameter in a multi-parameter exponential family. A condition is derived under which posterior Bayes quantiles match the conditional frequentist coverage to a higher-order approximation in terms of the sample size. This condition is on the model, not on the prior, and it ensures that any first-order probability matching prior in the unconditional sense automatically yields…

指数族推断中无条件参数自助法的条件性质AI 解读

Higher-order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping, in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family. The optimal test, which is approximated, is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter. A bootstrap procedure that ignores the conditioning is shown to have desirable conditional…

向量 M 估计目标的标量函数：高精度置信限AI 解读

This paper concerns high‐order inference for scalar parameters that are estimated by functions of multivariate M‐estimators. Asymptotic formulae for the bias and skewness of the studentised statistic are derived. Although these formulae appear complicated, they can be evaluated easily by using matrix operations and numerical differentiation. Various methods for constructing second‐order accurate confidence limits are discussed, including a method based on skewness‐reducing…

M估计中标量参数剖面经验似然函数的近似AI 解读

Empirical likelihood possesses many of the important properties of genuine parametric likelihood, but it is computationally burdensome, especially when nuisance parameters are present. This paper presents two approximations to the profile empirical likelihood function for a scalar parameter of interest in the context of M‐estimation; the simpler approximation is based on the third derivative of the profile log empirical likelihood function at its maximising point, while the…

边际尾概率近似与标量参数推断AI 解读

In many situations, inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density. For such inference, accurate approximations of marginal tail probabilities are useful to avoid high-dimensional integrals. Two tail probability approximations are developed in this paper. Numerical results given for conditional inference in location-scale and linear regression models…

线性回归模型的似然推断AI 解读

Approximate conditional inference based on large-sample likelihood ratio methods is considered for the parameters of linear regression models. Mean and variance adjustments that improve the standard normal approximation to the conditional distribution of the signed square root of the log-likelihood-ratio statistic for a scalar parameter of interest are given. A Bartlett adjustment factor that improves the chi-squared approximation to the conditional distribution of the…

线性回归模型的似然推断AI 解读

Approximate conditional inference based on large-sample likelihood ratio methods is considered for the parameters of linear regression models. Mean and variance adjustments that improve the standard normal approximation to the conditional distribution of the signed square root of the log-likelihood-ratio statistic for a scalar parameter of interest are given. A Bartlett adjustment factor that improves the chi-squared approximation to the conditional distribution of the…

参数变换与区间估计AI 解读

Parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large-sample theory are discussed for models depending on an unknown scalar parameter. Transformation formulae by which such parameterizations can be obtained are derived, and these formulae extend those for one-dimensional curved exponential families given by Hougaard (1982). To assess the accuracy of normal approximations to the distributions of the pivots, their…

参数变换与区间估计AI 解读

Parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large-sample theory are discussed for models depending on an unknown scalar parameter. Transformation formulae by which such parameterizations can be obtained are derived, and these formulae extend those for one-dimensional curved exponential families given by Hougaard (1982). To assess the accuracy of normal approximations to the distributions of the pivots, their…