To test heteroscedasticity in single index models, in this paper two test statistics are proposed via quadratic conditional moments. Without the use of dimension reduction structure, the first test has the usual convergence rate in nonparametric sense. Under the dimension reduction structure of...

We present a probability-integral-transformation-based estimator of multivariate densities. Given a sample of random vectors, we first transform the data into their corresponding marginal distributions. The marginal densities and the joint density of the transformed data are estimated...

Nonparametric density estimators on RK may fail to be consistent when the sample size n does not grow fast enough relative to reduction in smoothing. For example a Gaussian kernel estimator with bandwidths proportional to some sequence hn is not consistent if nhnK fails to diverge to infinity....

We design a data-dependent metric in Rd and use it to define the k-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual...

Suppose that U=(U1,…,Ud) has a Uniform([0,1]d) distribution, that Y=(Y1,…,Yd) has the distribution G on R+d, and let X=(X1,…,Xd)=(U1Y1,…,UdYd). The resulting class of distributions of X (as G varies over all distributions on R+d) is called the Scale Mixture of Uniforms class of...

Considering multivariate strongly mixing time series, nonparametric tests for a constant copula with specified or unspecified change point (candidate) are derived; the tests are consistent against general alternatives. A tapered block multiplier technique based on serially dependent multiplier...

Quintela-del-Río (2006) considered the estimation of the maximum hazard under dependence conditions and established strong convergence with rate and asymptotic normality of the estimate. The aim of this paper is to generalize this work to the case of right censored data with covariate. Via a...

Let (X, Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that...

In this paper, we provide a nonparametric estimator of the distribution of bivariate censored lifetimes, in a model where the two censoring variables differ only through an additional observed variable. This situation is motivated by a particular application to insurance, where the supplementary...