Note on asymptotic normality of kernel density estimator for linear process under short-range dependence

• Autorzy: Furmańczyk K.
• Języki publikacji: EN

Abstrakty

EN

We consider the problem of density estimation for a one-sided linear process [formula] with i.i.d. square integrable innovations [formula]. We prove that under weak conditions on [formula], which imply short-range dependence of the linear process, finite-dimensional distributions of kernel density estimate area symptotically multivariate normal. In particular, the result holds for |a_n|=θ(n^−a) 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_n→0 and nb_n→ ∞.The proof uses Chanda’s [1], [2] conditioning technique as well as Bernstein’s “large block-small block” argument.

Słowa kluczowe

EN

density estimator; linear process; proof Chanda’s

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 253--263
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Furmańczyk K.

• Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] K. C. Chanda, Density estimation for linear processes, Ann. Inst. Statist. Math. 35 (1983), pp. 439-446.
• [2] K. C. Chanda, Corrigendum to “Density estimation for linear processes", unpublished note.
• [3] L. Giraitis, H. L. Koul and D. Surgailis, Asymptotic Normality of regression estimators with long memory errors, Statist. Probab. Lett. 29, No 4 (1996), pp. 317-335.
• [4] M. Hallin and L. T. Tran, Kerne/ density estimation for linear processes: asymptotic normality and optimal bandwidth derivation, Ann. Inst. Statist. Math. 48 (1996), pp. 429-449.