On m out of n Bootstrapping for Nonstandard M-Estimation With Nuisance Parameters
On m out of n Bootstrapping for Nonstandard M-Estimation With Nuisance Parameters
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带有有害参数的非标准 M 估计的 n 中 m 引导
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
M. C Pun
中科院分区：
文献类型：
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作者：
Stephen M. S Lee;M. C Pun
非标准的M-估计，与滋扰参数一致估计的标准功能，往往会产生M-估计收敛弱的速度不同于n1/2的弱限制，通常是非高斯。所涉及的复杂的渐近性使得分布估计的M-估计解析禁止。我们证明了在非常一般的条件下，这个问题可以通过n中取m来解决，这为一致地估计M估计量的抽样分布提供了一种通用而方便的方法。我们说明了我们的研究结果与应用程序的最小中位数的平方回归估计，学生化的位置M-估计，短估计，和强大的M-估计来自LR型损失函数。我们提供了经验证据，使用模拟研究来构建置信区间和全局估计抽样分布。
Nonstandard M-estimation, with nuisance parameters consistently estimated in the criterion function, often yields M-estimators converging weakly at rates different from n1/2 with weak limits that are typically non-Gaussian. The complicated asymptotics involved makes distributional estimation of the M-estimators analytically prohibitive. We show that the problem is resolved by m out of n bootstrapping under very general conditions, which provides a universal and convenient approach to consistently estimating sampling distributions of M-estimators. We illustrate our findings with applications to least median of squares regression estimators, studentized location M-estimators, shorth estimators, and robust M-estimators derived from Lr-type loss functions. We provide empirical evidence using a simulation study to construct confidence intervals and globally estimate sampling distributions.