PARAMETER ESTIMATION IN A PARTLY LINEAR REGRESSION MODEL WITH RANDOM COEFFICIENT AUTOREGRESSIVE ERRORS

ABSTRACT

Consider a partly linear regression model where Y_i 's are responses, and are fixed design points, is an unknown parameter vector, is an unknown bounded real-valued function defined on a compact subset of the real line , and are unobservable random errors. We study the above model when is a first-order random coefficient autoregressive process, i.e., a stationary solution of , where {z_i } and {e_i } are zero mean independent processes each consisting of i.i.d. random variables with finite second moments and respectively. Various estimators of β, θ and are investigated and their limit distributions established. Consistent estimators of the covariance matrices of the various estimators of β are also proposed.

Keywords:

• Partly linear regression model
• Serially correlated errors
• Semiparametric generalized least squares estimator
• Asymptotic normality

ACKNOWLEDGMENT

The authors thank the three referees and the Editor for their helpful suggestions and comments which improved the presentation of the paper.