Abstract: We study the backfitting and profile methods for general criterion functions that depend on a parameter of interestand a nuisance function
. We show that when different amounts of smoothing are employed for each method to estimate the function
, the two estimation procedures produce estimators of
with the same limiting distributions, even when the criterion functions are non-smooth in
and/or
. 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.