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GENERAL LINEAR PROCESSES:A PROPERTY OF THE EMPIRICAL PROCESS APPLIED TO DENSITY AND MODE ESTIMATION
Author(s) -
Chanda K. C.,
Ruymgaart F. H.
Publication year - 1990
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1990.tb00051.x
Subject(s) - mathematics , estimator , corollary , rate of convergence , infimum and supremum , mixing (physics) , norm (philosophy) , mathematical optimization , uniform norm , econometrics , mathematical analysis , statistics , pure mathematics , computer science , law , computer network , channel (broadcasting) , physics , quantum mechanics , political science
. General linear processes do not usually satisfy strong mixing conditions. Therefore, we investigate the empirical process based on samples from such a general linear process by using a truncation argument and derive a local fluctuation inequality. It is well known that such a fluctuation inequality is of basic importance in the study of the empirical process. Here it is applied to obtain a rate of almost sure (a.s.) convergence for certain density estimators in the supremum norm. This extends a local result obtained by Chanda. As a direct corollary a rate of a.s. convergence for a mode estimator is obtained.