TRANSFORMATIONS FOR MULTIVARIATE STATISTICS
多元统计量的变换AI 解读 ↓
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多元统计量的变换
- 研究问题
- 能否通过变换消除多元统计量的渐近偏度，加快正态近似的收敛，并以较少计算获得与双重 bootstrap 相当的收敛速度？
- 方法与思路
- 作者在有效 Edgeworth 展开的框架下推导变换所需方程，提出满足目标阶数的局部解，并以指数模型及多类非线性回归进行说明。
- 材料陈述的贡献
- 摘要称，变换可消除展开的首个修正项，其 bootstrap 可达到原统计量双重 bootstrap 的收敛阶，从而节省计算。
- 阅读关注点
- 应核对展开有效性、局部解存在条件与余项阶数，并检查相同收敛阶如何证明，以及数值比较采用的误差指标和计算成本。
- 阅读边界
- 仅据所给 RePEc 出版社摘要解读；具体正则条件、误差阶和数值结果未列出，相同收敛阶不能直接说明所有样本下更准确。
原文摘要
This paper derives transformations for multivariate statistics that eliminate asymptotic skewness, extending the results of Niki and Konishi (1986, Annals of the Institute of Statistical Mathematics 38, 371–383). Within the context of valid Edgeworth expansions for such statistics we first derive the set of equations that such a transformation must satisfy and second propose a local solution that is sufficient up to the desired order. Application of these results yields two useful corollaries. First, it is possible to eliminate the first correction term in an Edgeworth expansion, thereby accelerating convergence to the leading term normal approximation. Second, bootstrapping the transformed statistic can yield the same rate of convergence of the double, or prepivoted, bootstrap of Beran (1988, Journal of the American Statistical Association 83, 687–697), applied to the original statistic, implying a significant computational saving.The analytic results are illustrated by application to the family of exponential models, in which the transformation is seen to depend only upon the properties of the likelihood. The numerical properties are examined within a class of nonlinear regression models (logit, probit, Poisson, and exponential regressions), where the adequacy of the limiting normal and of the bootstrap (utilizing the k-step procedure of Andrews, 2002, Econometrica 70, 119–162) as distributional approximations is assessed.This paper is derived from my Ph.D. thesis, “Higher-Order Asymptotics for Econometric Estimators and Tests,” for which thanks for patient and helpful supervision go to Grant Hillier. Comments by Karim Abadir, Francesco Bravo, Giovanni Forchini, Soren Johansen, Paul Marriott, Mark Salmon, and Steve Satchell, participants at the conference “Differential Geometric Methods in Econometrics,” held at EUI, Florence, and by two anonymous referees proved most helpful. In particular, I thank Peter Phillips for showing interest in the paper, helping with improving the exposition, and providing me with copies of two unpublished research notes. Financial support in the form of a Leverhulme Special Research Fellowship in Economics and Mathematics is gratefully acknowledged.