UNIFORM CONVERGENCE RATES FOR NONPARAMETRIC ESTIMATORS OF A DENSITY FUNCTION AND ITS DERIVATIVES WHEN THE DENSITY HAS A KNOWN POLE

We study the uniform convergence rates of nonparametric estimators for a probability density function and its derivatives when the density has a known pole. Such situations arise in some structural microeconometric models, for example, in auction, labor, and consumer search, where uniform convergence rates of density functions are important for nonparametric and semiparametric estimation. Existing uniform convergence rates based on Rosenblatt’s kernel estimator are derived under the assumption t