We propose a new test for independence of error and covariate in a nonparametric regression model. The test statistic is based on a kernel estimator for the L2-distance between the conditional distribution and the unconditional distribution of the covariates. In contrast to tests so far...

In this paper we consider the estimation of the error distribution in a heteroscedastic nonparametric regression model with multivariate covariates. As estimator we consider the empirical distribution function of residuals, which are obtained from multivariate local polynomial fits of the...

We suggest a method for reducing variance in nonparametric surface estimation. The technique is applicable to a wide range of inferential problems, including both density estimation and regression, and to a wide variety of estimator types. It is based on estimating the contours of a surface by...

We show that the coverage error of confidence intervals and level error of hypothesis tests for population quantiles constructed using the bootstrap estimate of sample quantile variance is of precise order n-1/2 in both one- and two-sided cases. This contrasts markedly with more classical...

We obtain a unform strong approximation for the distribution of a Nadaraya-Watson kernel estimator of a regression function. The approximation is obtained for general multivariate explanatory variables under an algebraic moment condition on the errors. A stronger rate of convergene result for...

It is often proposed (R. P. W. Duin, I.E.E.E. Trans. Comput.25 (1976), 1175-1179; J. D. F. Habbema, J. Hermans, and J. Remme, "Compstat 1978" (Corsten and Hermans, Eds.), pp. 178-185, "Compstat 1974" (G. Bruckman, Ed.), pp. 101-110;[16] and [17]) that Kullback-Leibler loss or likelihood...

Martingale theory is used to obtain a central limit theorem for degenerate U-statistics with variable kernels, which is applied to derive central limit theorems for the integrated square error of multivariate nonparametric density estimators. Previous approaches to this problem have employed...

We compare the merits of two orthogonal series methods of estimating a density and its derivatives on a compact interval--those based on Legendre polynomials, and on trigonometric functions. By examining the rates of convergence of their mean square errors we show that the Legendre polynomial...

The accuracy of the binned kernel density estimator is studied for general binning rules. We derive mean squared error results for the closeness of this estimator to both the true density and the unbinned kernel estimator. The binning rule and smoothness of the kernel function are shown to...

One way of estimating a function from indirect, noisy measurements is to regularise an inverse of its Fourier transformation, using properties of the adjoint of the transform that degraded the function in the first place. It is known that when the function is smooth, this approach can perform...