Weighted bootstrapped kernel density estimators in two-sample problems

Nonparametric density deconvolution by weighted kernel estimators

JSM, Denver, 4 August 2008 – 3 / 23 We observe a univariate random sample Y1, . . . , Yn from a density g, where Yi = Xi + Zi (i = 1, . . . , n). Here X1, . . . , Xn are independent and identically distributed with unknown continuous density f , and the measurement errors Z1, . . . , Zn form a random sample from the continuous density η which we assume to be known. Our goal is to obtain a nonpa...

Weighted Uniform Consistency of Kernel Density Estimators

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...

Kernel Density Estimators: Convergence in Distribution for Weighted Sup-norms

Let fn denote a kernel density estimator of a bounded continuous density f in the real line. Let Ψ(t) be a positive continuous function such that ‖Ψf‖∞<∞. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2 log h−1 n supt∈R ∣∣Ψ(t)(fn(t)−Efn(t))∣∣ (properly centered and normalized) to converge in distribution to the double exponential law are obtaine...

Deconvoluting Kernel Density Estimators

This paper considers estimation of a continuous bounded probability density when observations from the density are contaminated by additive measurement errors having a known distribution. Properties of the estimator obtained by deconvolving a kernel estimator of the observed data are investigated. When the kernel used is sufficiently smooth the deconvolved estimator is shown to be pointwise con...

Pruning kernel density estimators