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We study the backfitting and profile methods for general criterion functions that depend on a parameter of interest and a nuisance function 9. 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.
author list (cited authors)
Van Keilegom, I., & Carroll, R. J.