Backfitting versus profiling in general criterion functions

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.

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