Constructing Approximately Standard Normal Pivots from Signed Roots of Adjusted Likelihood Ratio Statistics
针对存在多余参数时标量参数的推断，本文提出通过均值和方差校正，基于调整似然比统计量的符号根构造近似标准正态枢轴量，使误差阶数从O(n^{-1/2})降至O(n^{-3/2})，并给出了通用公式和数值示例。
For inference about a scalar parameter *I in the presence of nuisance parameters, several authors have suggested that the usual log profile likelihood function M(41) be replaced by an objective function of the form M(*) = M(*) + B(*), where the derivatives of the adjustment function B(*) are of order Op(l). An adjusted likelihood ratio statistic W(4/) can be defined in terms of M(*). The distribution of R(qlD, the signed root of W(4), is typically standard normal to error of order O(n- /2). This paper concerns the use of mean and variance corrections to construct approximate pivots based on R(f) that have the standard normal distribution to error of order 0(n-3/2). General formulae for the mean and variance corrections are provided, and these formulae are evaluated for specific adjustment functions B(q) that have been proposed in the literature. Use of the corrections is illustrated in numerical examples.