The additive model with different smoothness for the components

2014/05/26 by Sara van de Geer, van de Geer, Sara, Alan Muro +1 · 1 citation
Decision Sciences · Mathematics · #62G08 #Advanced Statistical Process Monitoring #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1405.6584

openalex publication_date 2014/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an additive regression model consisting of two components f⁰ and g⁰, where the first component f⁰ is in some sense "smoother" than the second g⁰. Smoothness is here described in terms of a semi-norm on the class of regression functions. We use a penalized least squares estimator ( f, g) of (f⁰, g⁰) and show that the rate of convergence for f is faster than the rate of convergence for g. In fact, both rates are generally as fast as in the case where one of the two components is known. The theory is illustrated by a simulation study. Our proofs rely on recent results from empirical process theory.

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