On the Distance Between Smoothed Empirical and Quantile Processes

We consider Bahadur-Kiefer representations for smoothed quantile processes. We prove that the asymptotics of the distance between smoothed empirical and quantile processes can be completely different from that of the unsmoothed ones. We obtain a complete characterization of the possible limits.

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Bibliographische Detailangaben
Veröffentlicht in:	The Annals of statistics 1995-02, Vol.23 (1), p.113-131
Hauptverfasser:	Csorgo, Miklos, Horvath, Lajos
Format:	Artikel
Sprache:	eng
Schlagworte:	60F05 62G30 Approximation Bahadur-Kiefer representation Brownian bridge Distribution functions empirical process Estimators Exact sciences and technology Kernel-smoothing Mathematical theorems Mathematics Mean value theorems Non-parametric Inference Nonparametric inference Probabilities Probability and statistics quantile process Random variables Sciences and techniques of general use Statistics
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Beschreibung
Zusammenfassung:	We consider Bahadur-Kiefer representations for smoothed quantile processes. We prove that the asymptotics of the distance between smoothed empirical and quantile processes can be completely different from that of the unsmoothed ones. We obtain a complete characterization of the possible limits.
ISSN:	0090-5364 2168-8966
DOI:	10.1214/aos/1176324458