Subsampling quantile estimators and uniformity criteria |
| |
Authors: | WD Kaigh Cheng cheng |
| |
Institution: | 1. Department of mathematical sciences , University of texas at el paso , El paso, Texas 79968;2. Statistics department , Texas A&3. University , College station, Texas 77843 |
| |
Abstract: | Several asymptotically equivalent quantile estimators recently have been proposed as alternative to the conventional sample quantile. A variety of weight functions have been obtained either by subsampling considerations or by a kernel approach, analogous to density estimation techniques. Focusing on the former approach, a unified treatment of quantile estimators derived by subsampling is developed. Closely related to the generalized Harrell-Davis (HD) and Kaigh-Lachenbruch (KL) estimators, a new statistic performed well in Monte Carlo effiency comparisons presented here. Moreover, the new estimator shares certain desirable computational and finite-sample theeoretical properties with the KL estimator to yield convenient components representations for tests of uniformity and goodness-of-fit criteria. Similar analytic treatment for the HD statistics and kernel quantile estimators, however, is precluded by intractable eigenvalue problems. |
| |
Keywords: | empirical quantile function quantile estimation L-statistic U-statistic V-statistic quadratic tests |
|
|