“School of Biological Sciences”
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| Paper IPM / Biological Sciences / 14124 |
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| Abstract: | |||||
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This paper is concerned with the ridge estimation of the parameter vector β in partial linear
regression model y
i
= x
i
β +f (t
, 1 �?� i �?� n, with correlated errors, that is, when
Cov(ϵ) = �?
2
i
) +ϵ
i
V, with a positive definite matrix V and ϵ = (ϵ
), under the linear
constraint Rβ = r, for a given matrix R and a given vector r. The partial residual estimation
method is used to estimate β and the function f (·). Under appropriate assumptions,
the asymptotic bias and variance of the proposed estimators are obtained. A generalized
cross validation (GCV) criterion is proposed for selecting the optimal ridge parameter and
the bandwidth of the kernel smoother. An extension of the GCV theorem is established to
prove the convergence of the GCV mean. The theoretical results are illustrated by a real
data example and a simulation study.
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