Uniform convergence rates for nonparametric estimators smoothed by the beta kernel
Masayuki Hirukawa, Irina Murtazashvili, Artem Prokhorov
Abstract
Abstract This paper provides a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the beta kernel having support on the unit interval. Weak and strong uniform convergence is explored on the basis of expanding compact sets and general sequences of smoothing parameters. The results in this paper are useful for asymptotic analysis of two‐step semiparametric estimation using a first‐step kernel estimate as a plug‐in. We provide simulations and a real data example illustrating attractive properties of the estimators.
Topics & Concepts
MathematicsEstimatorKernel (algebra)Kernel smootherKernel density estimationSmoothingConsistency (knowledge bases)Nonparametric regressionNonparametric statisticsApplied mathematicsUniform convergenceVariable kernel density estimationRate of convergenceKernel regressionSemiparametric regressionConvergence (economics)Density estimationKernel methodStatisticsComputer scienceCombinatoricsDiscrete mathematicsChannel (broadcasting)Support vector machineBandwidth (computing)Artificial intelligenceEconomicsComputer networkRadial basis function kernelEconomic growthStatistical Methods and InferenceBayesian Methods and Mixture ModelsStatistical Methods and Bayesian Inference