In this paper we consider a nonparametric regression model that admits a mix of continuous and discrete regressors, some of which may in fact be redundant (that is, irrelevant). We show that, asymptotically, a data-driven least squares cross-validation method can remove irrelevant regressors....

Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the...

Motivated by applications in high-dimensional settings, we suggest a test of the hypothesis H-sub-0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may...

One of the attractions of crossvalidation, as a tool for smoothing-parameter choice, is its applicability to a wide variety of estimator types and contexts. However, its detractors comment adversely on the relatively high variance of crossvalidatory smoothing parameters, noting that this...

We point out that inliers adversely affect performance of the spatial median and its generalization due to Gentleman. They are most deleterious in the case of the median itself, and in the important setting of two dimensions. There, the second term in a stochastic expansion of the median has a...

We construct a simple algorithm, based on Newton's method, which permits asymptotic minimization of L1 distance for nonparametric density estimators. The technique is applicable to multivariate kernel estimators, multivariate histogram estimators, and smoothed histogram estimators such as...

We describe a bootstrap method for estimating mean squared error and smoothing parameter in nonparametric problems. The method involves using a resample of smaller size than the original sample. There are many applications, which are illustrated using the special cases of nonparametric density...

For a sequence of independent and identically distributed random vectors, upper and lower bounds are obtained for the discrepancy between the probability measure Pn, induced by their normalized sum, and the Normal measure [Phi]. The upper and lower bounds are of the same order of magnitude....

The usuall form of cross-validation is global in character, and is designed to estimate a density in some "average" sense over its entire support. In this paper we present a local version of squared-error cross-validation, suitable for estimating a probability density at a given point. It is...