Inverse boosting for monotone regression functions

Authors:
Yuwon Kim;Ja-Yong Koo
Affiliations:
Statistical Research Center for Complex Systems, Seoul National University, Kwan Ak Gu, Sillim dong, Seoul 151-742, Republic of Korea;Department of Statistics, Inha University, Incheon 402-751,Republic of Korea
Venue:
Computational Statistics & Data Analysis
Year:
2005

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Abstract

A new method for the estimation of smooth monotone regression functions is proposed. It is assumed that the monotonicity may come from some physical or economic reason. A monotone estimator of an integral (of a positive function) using a gradient boosting method is derived. The proposed method generates a sequence of fits without monotone constraints and combines them to form a monotone estimate. An advantage of the proposed algorithm is that one can use a popular smoothing technique without the monotone constraint as the base learner. The performance of the proposed procedure is demonstrated on both simulated and real data sets.