On the asymptotic mean integrated squared error of a kernel density estimator for dependent data

Jan Mielniczuk

Abstract

Hall and Hart (1990) proved that the mean integrated squared error (MISE) of a marginal kernel density estimator from an infinite moving average process X1, X2, … may be decomposed into the sum of MISE of the same kernel estimator for a random sample of the same size and a term proportional to the variance of the sample mean. Extending this, we show here that the phenomenon is rather general: the same result continues to hold if dependence is quantified in terms of the behaviour of a remainder term in a natural decomposition of the densities of (X1, X1+i), i = 1, 2, ….
Author Jan Mielniczuk (FMIS / DSPFM) - [Instytut Podstaw Informatyki Polskiej Akademii Nauk (IPI PAN) [Polish Academy of Sciences (PAN)]]
Jan Mielniczuk,,
- Department of Stochastic Processes and Financial Mathematics
- Instytut Podstaw Informatyki Polskiej Akademii Nauk
Journal seriesStatistics & Probability Letters, [Statistics and Probability Letters], ISSN 0167-7152, e-ISSN 1879-2103
Issue year1997
Vol34
No1
Pages53-58
Publication size in sheets0.5
Keywords in EnglishKernel estimator; Long-range dependence; Mean integrated square error
ASJC Classification1804 Statistics, Probability and Uncertainty; 2613 Statistics and Probability
DOIDOI:10.1016/S0167-7152(96)00165-4
URL https://www.sciencedirect.com/science/article/pii/S0167715296001654
Languageen angielski
Score (nominal)15
Score sourcejournalList
Publication indicators WoS Citations = 11; GS Citations = 12.0; Scopus SNIP (Source Normalised Impact per Paper): 1999 = 0.735; WoS Impact Factor: 2006 = 0.286 (2) - 2007=0.443 (5)
Citation count*12 (2015-02-21)
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