2006/12/31 by Vivian Viallon
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Financial Risk and Volatility Modeling #Statistical Methods and Inference #math.ST #msc:60F15 #msc:60F17 #msc:62G07 #stat.TH
paper · pdf · doi:10.1214/07-ejs099
published as Electronic Journal of Statistics 2007, Vol. 1, 496-518 · Published in at http://dx.doi.org/10.1214/07-EJS099 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/01/01 · arxiv created 2007/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size n→∞. We extend a limit law obtained by Deheuvels and Mason [12], showing that their results hold uniformly over the bandwidth h, restricted to vary in [h'n,h''n], where h'nn≥1 and h''nn≥1 are appropriate non-random sequences. We treat the case where the sample observations follow possibly non-uniform distributions. As a consequence of our theorems, we provide uniform limit laws for nearest-neighbor density estimators, in the spirit of those given by Deheuvels and Mason [13] for kernel-type estimators.