Consistencies and rates of convergence of jump-penalized least squares estimators

L. Boysen, A. Kempe, V. Liebscher, A. Munk, O. Wittich

Research output: Contribution to journalArticleAcademicpeer-review

81 Citations (Scopus)
193 Downloads (Pure)

Abstract

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in L2([0, 1)) our results cover other metrics like Skorokhod metric on the space of càdlàg functions and uniform metrics on C([0, 1]). We will show that these estimators are in an adaptive sense rate optimal over certain classes of "approximation spaces." Special cases are the class of functions of bounded variation (piecewise) Hölder continuous functions of order 0
Original languageEnglish
Pages (from-to)157-183
JournalThe Annals of Statistics
Volume37
Issue number1
DOIs
Publication statusPublished - 2009

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