刻度函数的稳健估计方法

ROBUST ESTIMATORS OF SCALE FUNCTION

在对统计数据的建模和分析中,数据的波动性和扰动性是人们越来越关注的一个问题.于是如何对其进行有效地识别和刻画并精确地估计出来就变得尤为重要.文章考虑一个线性异方差模型,主要的目标是将未知的刻度函数稳健地恢复出来.在传统的刻度参数的估计中,四分位距是一个稳健的估计量.文章在此基础上进一步提出"极小四分位距"及"最优分位距"两个新的稳健估计量,欲将任意分布F中的刻度参数有效地估计出来.进而为了对异方差模型中的刻度函数进行估计,将该思想推广到条件分布中,并利用分位回归技术,这样刻度函数就得以稳健的恢复出来.值得说明的是在估计过程中无需知道均值函数的任何信息,使得该方法更具优势.此外文章研究了估计量的渐近性质并与传统的四分位距方法进行比较.结果表明,不论误差分布是对称的还是非对称的,所提出的估计量都有显著的优越性.最后,为了检测所提出估计量的性能,进行了一些模拟研究,得到的结果与理论是相符的.

In the analysis and modelling of statistical data, variation and volatility of which are becoming more concerned. Thus, it is crucial to effectively detect and exactly estimate this variation. In this paper, a linear heteroscedastic model is mainly considered. The aim is to recover the unknown scale function robustly. As is known, interquartile range is a robust estimator in classical estimation of scale parameter. Based on this, ＂minimal interquartile range＂ and ＂optimal quantile range＂ estimators are proposed to effectively estimate the scale parameter of unknown probability distribution F. Besides, in order to obtain the scale function of a linear heteroscedastic model, we generalize this idea to conditional distribution and apply quantile regression techniques simultaneously. It is worth noting that information of mean regression function is not required in estimation, which makes the proposed approach superior. In addition, asymptotic properties of proposed estimators are studied and comparisons with classical interquartile range are made. The results show that our proposed estimators perform better under both symmetric and asymmetric distributions. In the end, simulations are conducted to examine the performance of our methods.