Optimal bandwidth selection rule for kernel regression estimator with dependent variables

Let $\{$(X$\sb{\rm t}$,Y$\sb{\rm t}$): t $\in$ N$\}$ be a strictly stationary process with X$\sb{\rm t}$ being R$\sp{\rm d}$-valued and Y$\sb{\rm t}$ being real valued. Consider the problem of estimating the conditional expectation function, m(x) = E(Y$\sb{\rm t}\vert$ X$\sb{\rm t}$ = x), using (X$\sb1,$Y$\sb1$),$\...$ (X$\sb{\rm n}$,Y$\sb{\rm n}$). (For example, suppose Z$\sb{\rm t}$, t = 0, $\pm$1, $\pm$2,.. is a real valued stationary time series and p is a positive integer. Set X$\sb{\rm t}$ = (Z$\sb{\rm t+1},\...$,Z$\sb{\rm t+d}$) and Y$\sb{\rm t}$ = Z$\sb{\rm t+d+p}$. Then (X$\sb{\rm t}$,Y$\sb{\rm t}$), t = 0, $\pm$1,.. is a stationary time series and m(x) = E(Z$\sb{\rm d+p}\vert$Z$\sb1,\...$Z$\sb{\rm d}$).) We consider kernel estimators of m(x). Recently, convergence properties of the kernel estimator have been developed under certain dependence structures for the process (X$\sb{\rm t}$,Y$\sb{\rm t}$). One of the crucial points in applying a kernel estimator is the choice of bandwidth. The main purpose of this work is to establish asymptotic optimality for a bandwidth selection rule under dependence which can be interpreted in terms of cross validation. In addition, some moment bounds for dependent variables will be established, which give more flexible bounds than existing ones.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Kim, Tae Yoon

Contributors dc:contributor

• Cox, Dennis D.

• Statistics

Statement dc:rights

• Copyright 1990 Kim, Tae Yoon

Language dc:language

eng

Identifier

AAI9026227
(UMI)AAI9026227

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/19451