標題: | Symmetric regression quantile and its application to robust estimation for the nonlinear regression model |
作者: | Chen, LA Tran, LT Lin, LC 統計學研究所 Institute of Statistics |
關鍵字: | nonlinear regression;regression quantile;trimmed mean |
公開日期: | 1-十二月-2004 |
摘要: | Populational conditional quantiles in terms of percentage alpha are useful as indices for identifying outliers. We propose a class of symmetric quantiles for estimating unknown nonlinear regression conditional quantiles. In large samples, symmetric quantiles are more efficient than regression quantiles considered by Koenker and Bassett (Econometrica 46 (1978) 33) for small or large values of alpha, when the underlying distribution is symmetric, in the sense that they have smaller asymptotic variances. Symmetric quantiles play a useful role in identifying outliers. In estimating nonlinear regression parameters by symmetric trimmed means constructed by symmetric quantiles, we show that their asymptotic variances can be very close to (or can even attain) the Cramer-Rao lower bound under symmetric heavy-tailed error distributions, whereas the usual robust and nonrobust estimators cannot. (C) 2003 Elsevier B.V. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.jspi.2003.09.014 http://hdl.handle.net/11536/25622 |
ISSN: | 0378-3758 |
DOI: | 10.1016/j.jspi.2003.09.014 |
期刊: | JOURNAL OF STATISTICAL PLANNING AND INFERENCE |
Volume: | 126 |
Issue: | 2 |
起始頁: | 423 |
結束頁: | 440 |
顯示於類別: | 期刊論文 |