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Spline smoothing in a partly linear model. (English) Zbl 0623.62030
The following model is considered: \[ Y_ i=X_ i'\beta +f(t_ i)+e_ i, \] where the errors \(e_ i\) are independently and identically distributed with zero means, \(\beta\) is an unknown k-vector and f is an unknown mapping from \({\mathbb{R}}\) into \({\mathbb{R}}\) of which the m-th derivative is square integrable.
The problem of estimating \(\beta\) and f is considered through the minimization of a criterium which is the sum of two terms, the residual sum of squares and a measure of smoothness of f.
Consistency and asymptotic normality of \({\hat \beta}\) are studied; moreover it is shown that \({\hat \beta}\) and \(\hat f\) are the Bayes estimates under some prior distribution.
Reviewer: J.-R.Mathieu

MSC:
62G05 Nonparametric estimation
62J99 Linear inference, regression
62F15 Bayesian inference
62E20 Asymptotic distribution theory in statistics
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