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Testing serial correlation in semiparametric varying-coefficient partially linear EV models

Testing serial correlation in semiparametric varying-coefficient partially linear EV models This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X τ β + Z τ α(T) + ε, ξ = X + η with the identifying condition E[(ε, η τ ) τ ] = 0, Cov[(ε, η τ ) τ ] = σ 2 I p+1. The estimators of interested regression parameters β, and the model error variance σ 2, as well as the nonparametric components α(T), are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ 2 are strongly consistent and asymptotically normal and that the estimator of α(T) achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the V N,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Testing serial correlation in semiparametric varying-coefficient partially linear EV models

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer-Verlag
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-006-6168-1
Publisher site
See Article on Publisher Site

Abstract

This paper studies estimation and serial correlation test of a semiparametric varying-coefficient partially linear EV model of the form Y = X τ β + Z τ α(T) + ε, ξ = X + η with the identifying condition E[(ε, η τ ) τ ] = 0, Cov[(ε, η τ ) τ ] = σ 2 I p+1. The estimators of interested regression parameters β, and the model error variance σ 2, as well as the nonparametric components α(T), are constructed. Under some regular conditions, we show that the estimators of the unknown vector β and the unknown parameter σ 2 are strongly consistent and asymptotically normal and that the estimator of α(T) achieves the optimal strong convergence rate of the usual nonparametric regression. Based on these estimators and asymptotic properties, we propose the V N,p test statistic and empirical log-likelihood ratio statistic for testing serial correlation in the model. The proposed statistics are shown to have asymptotic normal or chi-square distributions under the null hypothesis of no serial correlation. Some simulation studies are conducted to illustrate the finite sample performance of the proposed tests.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 13, 2008

References