# zbMATH — the first resource for mathematics

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