Weighted Uniform Consistency of Kernel Density Estimators

  title={Weighted Uniform Consistency of Kernel Density Estimators},
  author={Evarist Gin{\'e} and Vladimir Koltchinskii and Joel Zinn},
Let fn denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let (t) be a positive continuous function such that‖ f β‖∞ < ∞ for some 0< β < 1/2. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2| loghn | ‖ (t)(fn(t) − Efn(t))‖∞ to be stochastically bounded and to converge a.s. to a constant are obtained. Also, the case of larger values of β is studied where a similar sequence with a different norming… CONTINUE READING