Optimal bandwidth selection rule for kernel regression estimator with dependent variables

Kim, Tae Yoon

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https://hdl.handle.net/2142/19451 Copy

Description

Title

Optimal bandwidth selection rule for kernel regression estimator with dependent variables

Author(s)

Kim, Tae Yoon

Issue Date

1990

Doctoral Committee Chair(s)

Cox, Dennis D.

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Statistics

Language

eng

Abstract

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.

Type of Resource

text

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http://hdl.handle.net/2142/19451

Copyright and License Information

Copyright 1990 Kim, Tae Yoon

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