Abstract
Consider the regression modely i =ζ T i β+m(t i )+ε i fori=1,...,n. Here (ζ T i ,t i )T∈ℝp×[0,1] are design points, β is an unknownp×1 vector of parameters,m is an unknown smooth function from [0,1] to ℝ andε i are the unobserved errors. We will assume that these errors are not independent. Under suitable assumptions, we obtain expansions for the bias and the variance of a Generalized Least Squares (GLS) type regression estimator, and for an estimator of the nonparametric functionm(·). Furthermore, we prove the asymptotic normality of the first estimator. The obtained results are a generalization of those contained in Speckman (1988), who studied a similar model with i.i.d. error variables.
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Research supported by the Xunta de Galicia (Spain) and the DGES (Spain) under research projects XUGA 10503A98 and PB98-0182-c02-01, respectively.
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Aneiros, G., Quintela, A. Asymptotic properties in partial linear models under dependence. Test 10, 333–355 (2001). https://doi.org/10.1007/BF02595701
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DOI: https://doi.org/10.1007/BF02595701