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

✍ Scribed by Jan Mielniczuk

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
357 KB
Volume
34
Category
Article
ISSN
0167-7152

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✦ Synopsis

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, )(2 .... 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, Xl+i), i = 1, 2 .....

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