GENERAL LINEAR PROCESSES:A PROPERTY OF THE EMPIRICAL PROCESS APPLIED TO DENSITY AND MODE ESTIMATION

K. C. Chanda and F. H. Ruymgaart

Journal of Time Series Analysis, 1990, vol. 11, issue 3, 185-199

Abstract: Abstract. 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.

Date: 1990
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https://doi.org/10.1111/j.1467-9892.1990.tb00051.x

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Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:11:y:1990:i:3:p:185-199

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