Statistica Sinica 19 (2009), 1463-1478

WAVELET-BASED BAYESIAN ESTIMATION OF

PARTIALLY LINEAR REGRESSION MODELS

WITH LONG MEMORY ERRORS

Kyungduk Ko$^1$, Leming Qu$^1$ and Marina Vannucci$^2$

$^1$Boise State University and $^2$Rice University

Abstract: In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.

Key words and phrases: Bayesian inference, long memory, MCMC, partially linear regression model, wavelet transforms.