ABSTRACT
Consider a partly linear regression model where Yi
'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 {zi
} and {ei
} 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.
ACKNOWLEDGMENT
The authors thank the three referees and the Editor for their helpful suggestions and comments which improved the presentation of the paper.