Non-crossing non-parametric estimates of quantile curves
成果类型：
Article
署名作者：
Dette, Holger; Volgushev, Stanislav
署名单位：
Ruhr University Bochum
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1111/j.1467-9868.2008.00651.x
发表日期：
2008
页码：
609-627
关键词：
摘要：
Since the introduction by Koenker and Bassett, quantile regression has become increasingly important in many applications. However, many non-parametric conditional quantile estimates yield crossing quantile curves (calculated for various p is an element of (0, 1)). We propose a new non-parametric estimate of conditional quantiles that avoids this problem. The method uses an initial estimate of the conditional distribution function in the first step and solves the problem of inversion and monotonization with respect to p is an element of (0, 1) simultaneously. It is demonstrated that the new estimates are asymptotically normally distributed with the same asymptotic bias and variance as quantile estimates that are obtained by inversion of a locally constant or locally linear smoothed conditional distribution function. The performance of the new procedure is illustrated by means of a simulation study and some comparisons with the currently available procedures which are similar in spirit with the method proposed are presented.