Density estimation for a class of stationary nonlinear processes

Autor:	Kamal C. Chanda
Rok vydání:	2003
Předmět:	Statistics and Probability Combinatorics Independent and identically distributed random variables Kernel (set theory) Convergence of random variables Calculus Density estimation Type (model theory) Random variable Realization (systems) Mathematics Central limit theorem
Zdroj:	Annals of the Institute of Statistical Mathematics. 55:69-82
ISSN:	1572-9052 0020-3157
DOI:	10.1007/bf02530485
Popis:	Let {X t ;t∈ℤ be a strictly stationary nonlinear process of the formX t =e t +∑ r=1 ∞ W rt , whereW rt can be written as a functiong r (e t−1,...e t-r-q ), {e t ;t∈ℤ is a sequence of independent and identically distributed (i.i.d.) random variables withE|e1| g 0 andq≥0 is fixed integer. Under certain mild regularity conditions ofg r and {e t } we then show thatX 1 has a density functionf and that the standard kernel type estimator\(\hat f_n (x)\) baded on a realization {X 1,...,X n } from {X t } is, asymptotically, normal and converges a.s. tof(x) asn→∞.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::674b2bedb8c8861e2da95b26b9a7ee96 https://doi.org/10.1007/bf02530485 Zobrazit plný text záznamu Full text from SpringerLink