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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 21, Fasc. 2,
pages 253 - 263
 

NOTE ON ASYMPTOTIC NORMALITY OF KERNEL DENSITY ESTIMATOR FOR LINEAR PROCESS UNDER SHORT-RANGE DEPENDENCE

Konrad Furmańczyk

Abstract: We consider the problem of density estimation for a one-sided linear process X = sum o o a Z t r=0 r t-r with i.i.d. square integrable innovations (Z ) oo . ii=- oo We prove that under weak conditions on (a ) oo , ii=0 which imply short-range dependence of the linear process, finite-dimensional distributions of kernel density estimate are asymptotically multivariate normal. In particular, the result holds for |a |= O(n-a) n with a > 2, which is much weaker than previously known sufficient conditions for asymptotic normality. No conditions on bandwidths b n are assumed besides b --> 0 n and nb -- > oo . n The proof uses Chanda’s [1], [2] conditioning technique as well as Bernstein’s “large block-small block” argument.

1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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