We consider estimation of the common probability density f of i.i.d. random variables Xi that are observed with an additive i.i.d. noise. We assume that the unknown density f belongs to a class A of densities whose characteristic function is described by the exponent exp(−α|u|r) as |u| → ∞, where α > 0, r > 0. The noise density is supposed to be known and such that its characteristic function d...

Bifurcating Markov chains are indexed by a full binary tree representing the evolution of trait along population where each individual has two children. Motivated functional estimation density invariant probability measure which appears as asymptotic distribution trait, we prove consistency and Gaussian fluctuations for kernel estimator this based on late generations. In setting, it is interest...

Fitting distributions of travel-time in vehicle traffic is an important application of spatio-temporal data mining. While regression methods to forecast the expected travel-time are standard approaches of travel-time prediction, we need to estimate distributions of the travel-time when using stateof-the-art risk-sensitive route recommendation systems. The authors introduce a novel nonparametric...

In the usual right-censored data situation, let fn, n∈N, denote the convolution of the Kaplan-Meier product limit estimator with the kernels a−1 n K(·/an), where K is a smooth probability density with bounded support and an→0. That is, fn is the usual kernel density estimator based on Kaplan-Meier. Let f̄n denote the convolution of the distribution of the uncensored data, which is assumed to hav...

This paper discusses modiications of the convolution type kernel regression estimator. One modiication uses kernel quantile estimators and is analyzed more detailed. This regression estimator combines advantages of local polynomial and kernel regression estimators and can be applied for small to large sample size. Its properties are illustrated by simulation results and asymptotic theory. Espec...

We are concerned with kernel density estimation on the rotation group SO(3). We prove asymptotically optimal convergence rates for the minimax risk of the mean integrated squared error for different function classes including bandlimited functions, functions with bounded Sobolev norm and functions with polynomial decaying Fourier coefficients and give optimal kernel functions. Furthermore, we c...

We consider kernel estimation of a univariate density whose support is a compact interval. If the density is non-zero at either boundary, then the usual kernel estimator can be seriously biased. "Reflection" at a boundary removes some bias, but unless the first derivative of the density is o at the boundary, the estimator with reflection can still be much more severely biased at the boundary th...