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标量参数的方差稳定化AI 解读

Summary We present a variance stabilizing transformation for inference about a scalar parameter that is estimated by a function of a multivariate M-estimator. The transformation proposed is automatic, computationally simple and can be applied quite generally. Though it is based on an intuitive notion and entirely empirical, the transformation is shown to have an appropriate justification in providing variance stabilization when viewed from both parametric and nonparametric…

通常似然与调整似然所构造多维置信集的期望体积AI 解读

Summary We consider a general multiparameter set-up, where both the interest and the nuisance parameters are possibly vector valued. We derive an explicit higher order asymptotic formula to compare the expected volumes of confidence sets given by likelihood ratio statistics arising from the usual profile likelihood and various adjustments thereof. Our general framework also allows us to include highest posterior density regions, with approximate frequentist validity, in the…

结合模拟与渐近近似计算贝叶斯因子AI 解读

The Bayes factor is a ratio of two posterior normalizing constants, which may be difficult to compute. We compare several methods of estimating Bayes factors when it is possible to simulate observations from the posterior distributions, via Markov chain Monte Carlo or other techniques. The methods that we study are all easily applied without consideration of special features of the problem, provided that each posterior distribution is well behaved in the sense of having a…

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近似贝叶斯推断的 Bartlett 调整AI 解读

In wide generality, the posterior distributions of the likehood ratio statistic and the posterior ratio statistic are chi-squared to error of order O(n−1), where n is sample size. The error in the chi-squared approximation can be reduced to order O(n−2) by Bartlett correction. In this paper, explicit formulae are derived for the Bartlett adjustment factors of both statistics, and the derivations are based on the Tierney. Kass & Kadane (1989) asymptotic approximation for…

似然比统计量带符号根的简易修正AI 解读

SUMMARY In the context of inference about a scalar parameter in the presence of nuisance parameters, some simple modifications for the signed root of the log-likelihood ratio statistic R are developed that reduce the order of error in the standard normal approximation to the distribution of R from O(n -1/2) to O(n -1). Barndorff-Nielsen has introduced a variable U such that the error in the standard normal approximation to the distribution of R + R -1 log(U/R) is of order…

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近似贝叶斯推断中的 Bartlett 调整AI 解读

In wide generality, the posterior distributions of the likehood ratio statistic and the posterior ratio statistic are chi-squared to error of order O(n−1), where n is sample size. The error in the chi-squared approximation can be reduced to order O(n−2) by Bartlett correction. In this paper, explicit formulae are derived for the Bartlett adjustment factors of both statistics, and the derivations are based on the Tierney. Kass & Kadane (1989) asymptotic approximation for…

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快速且准确的近似双重自助法置信区间AI 解读

We propose two new methods for the construction of approximate iterated bootstrap confidence intervals. Our methods follow a saddlepoint approach, but employ approximate rather than exact solutions to the nonlinear saddlepoint equations that arise in applying that technique. The main advantages of the new techniques are that they yield confidence intervals with high coverage accuracy in small- to moderately-sized samples and that they achieve this accuracy with very…

一类光滑函数的边际尾概率近似及其在贝叶斯与条件推断中的应用AI 解读

This paper presents an asymptotic approximation of marginal tail probabilities for a real-valued function of a random vector, where the function has continuous gradient that does not vanish at the mode of the joint density of the random vector. This approximation has error O(n−3/2) and improves upon a related standard normal approximation which has error O(n−½). Derivation involves the application of a tail probability formula given by DiCiccio, Field & Fraser (1990) to an…

删失数据线性回归模型的精确近似条件推断与贝叶斯推断方法AI 解读

A method to approximate marginal posterior distribution functions of regression coefficients and scale parameters is presented. It is based on a general asymptotic formula of DiCiccio, Field & Fraser (1990) for approximating marginal tail probabilities. In developing the method, it is shown that the accuracy of the approximation of DiCiccio et al. can be substantially increased in certain cases by using a suitable change of variables, and a general approach to deriving such…

删失数据线性回归的精确近似条件推断与贝叶斯推断AI 解读

A method to approximate marginal posterior distribution functions of regression coefficients and scale parameters is presented. It is based on a general asymptotic formula of DiCiccio, Field & Fraser (1990) for approximating marginal tail probabilities. In developing the method, it is shown that the accuracy of the approximation of DiCiccio et al. can be substantially increased in certain cases by using a suitable change of variables, and a general approach to deriving such…

光滑函数边际尾概率的近似及其贝叶斯与条件推断应用AI 解读

This paper presents an asymptotic approximation of marginal tail probabilities for a real-valued function of a random vector, where the function has continuous gradient that does not vanish at the mode of the joint density of the random vector. This approximation has error O(n−3/2) and improves upon a related standard normal approximation which has error O(n−½). Derivation involves the application of a tail probability formula given by DiCiccio, Field & Fraser (1990) to an…

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平滑与自助法AI 解读

Recent attention has focussed on possible improvements in performance of estimators which might flow from using the smoothed bootstrap. We point out that in a great many problems, such as those involving functions of vector means, any such improvements will be only second-order effects. However, we argue that substantial and significant improvements can occur in problems where local properties of underlying distributions play a decisive role. This situation often occurs in…

参数似然与经验似然函数的比较AI 解读

In this paper, parametric and empirical likelihood functions or surfaces are compared. In particular, first- and second-order expansions for log likelihood functions are developed in nonparametric and parametric situations, where the functional of interest is a smooth function of vector means. The two approaches are compared and the precise order of difference between the nonparametric and parametric log likelihood functions is obtained. In general, the surfaces need not…

基于经验似然比统计量带符号平方根的调整AI 解读

The standard multivariate normal approximation to the distribution of the signed root of the empirical likelihood ratio statistic is considered in cases where inference is required for a smooth function of the mean of the distribution from which the sample is drawn. The error in this approximation is of order O(n−½) where n is the sample size, and it is shown that the error can be reduced to order O(n−1) by using a mean adjustment. When a scalar parameter is of interest, use…

自助法置信区间综述AI 解读

SUMMARY A survey of bootstrap procedures for constructing confidence regions is given. In particular, several distinct bootstrap methods are considered, with emphasis on the mathematical correctness of these procedures. The percentile, bias-corrected percentile and accelerated bias-corrected percentile methods, developed by Efron, are reviewed in both parametric and nonparametric situations. A procedure related to the accelerated bias-corrected method, which avoids explicit…