Statistica Sinica 17(2007), 797-816

BACKFITTING VERSUS PROFILING IN GENERAL

CRITERION FUNCTIONS

Ingrid Van Keilegom and Raymond J. Carroll

Université catholique de Louvain and Texas A &M University

Abstract: We study the backfitting and profile methods for general criterion functions that depend on a parameter of interest $\beta$ and a nuisance function $\theta$. We show that when different amounts of smoothing are employed for each method to estimate the function $\theta$, the two estimation procedures produce estimators of $\beta$ with the same limiting distributions, even when the criterion functions are non-smooth in $\beta$ and/or $\theta$. The results are applied to a partially linear median regression model and a change point model, both examples of non-smooth criterion functions.

Key words and phrases: Backfitting, change points, dioxin, kernel estimation, median regression, nonparametric regression, partially linear model, profile kernel methods, semiparametric estimation, undersmoothing.