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General Linear Processes:A Property Of The Empirical Process Applied To Density And Mode Estimation

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  • K. C. Chanda
  • F. H. Ruymgaart

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.

Suggested Citation

  • K. C. Chanda & F. H. Ruymgaart, 1990. "General Linear Processes:A Property Of The Empirical Process Applied To Density And Mode Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(3), pages 185-199, May.
    • Handle: RePEc:bla:jtsera:v:11:y:1990:i:3:p:185-199
    DOI: 10.1111/j.1467-9892.1990.tb00051.x
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