島根大学総合理工学部紀要.シリーズB

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島根大学総合理工学部紀要.シリーズB 47
2014-03 発行

Symptotics for penalized splines in additive models

吉田 拓真
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内容記述(抄録等)
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.