Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Rate of Convergence of Empirical Distributions and Quantiles in Linear Processes with Applications to Trimmed Mean

  • Lee, Sangyeol (Department of Statistics, Seoul National University)
  • Published : 1999.12.01
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Abstract

A 'convergence in probability' rate of the empirical distributions and quantiles of linear processes is obtained. As an application of the limit theorems, a trimmed mean for the location of the linear process is considered. It is shown that the trimmed mean is asymptotically normal. A consistent estimator for the asymptotic variance of the trimmed mean is provided.

Keywords

References

  1. Journal of Multivariate Analysis v.8 On Deviations between empirical and quantile processes for mixing random variables Babu, G. J.;Singh, K.
  2. Dependence in Probability and Statistics Basic properties of strong mixing conditions Bradley, R. C.;E. Eberein(ed.);M. S. Taqqued(ed.)
  3. South African Statististics Journal v.8 An asymptotic representation of trimmed means with application de Wet, T.;Venter, J. H.
  4. Australian Journal of Statististics v.30A Rate of convergence for the quantile function of a linear process Hannan, E. J.;Hesse, C. H.
  5. Journal of Multivariate Analysis v.35 Rates of convergence for the empirical distribution function and the empirical characteristic function of a broad class of linear processes Heese, C. H.
  6. Journal of Statistical Planning and Inferences v.48 A trimmed mean of location of an AR(∞) stationary process Lee, S.
  7. Zeit. Wahrsch. Werw. Gebiete v.30 Invariance principles for dependent variables McLeish, D. L.