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Paper IPM / Biological Sciences / 14124  


Abstract:  
This paper is concerned with the ridge estimation of the parameter vector Î² in partial linear
regression model y
i
= x
i
Î² +f (t
, 1 ï¿½?ï¿½ i ï¿½?ï¿½ n, with correlated errors, that is, when
Cov(Ïµ) = ï¿½?
2
i
) +Ïµ
i
V, with a positive definite matrix V and Ïµ = (Ïµ
), under the linear
constraint RÎ² = r, for a given matrix R and a given vector r. The partial residual estimation
method is used to estimate Î² and the function f (Â·). 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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