Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics

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Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 47
2014-03 発行

Symptotics for penalized splines in additive models

Yoshida, Takuma
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This paper is based on the author's thesis, Asymptotic theory of penalized spline regression. The focus of the present paper is on the penalized spline estimators obtained by the backfitting algorithm in additive models. The convergence of the algorithm as well as the uniqueness of its solution are shown. Asymptotic equivalence between the penalized spline estimators by the backfitting algorithm and the convenient estimators proposed by Marx and Eilers [9] is addressed. Asymptotic normality of the estimators is also developed.