This article extends recent developments in penalized likelihood probability density estimation to the estimation of conditional densities on generic domains. Positivity and unity constraints for a probability density are enforced through a one-to-one logistic conditional density transform made possible by term trimming in an ANOVA decomposition of multivariate functions. The construction of mo...

In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on certifying breadth-one singular solutions of polynomial systems, to compute verified and narrow error bounds such that a slightly perturbed system is guaranteed to possess an isolated singular solution within the computed bounds. Our new verification method is based on deflation techniques...

Kernel smoothing in nonparametric autoregressive schemes ooers a powerful tool in modelling time series. In this paper it is shown that the bootstrap can be used for estimating the distribution of kernel smoothers. This can be done by mimicking the stochastic nature of the whole process in the bootstrap resampling or by generating a simple regression model. Consistency of these bootstrap proced...

This is a survey of recent developments in smoothing parameter selection for curve estimation. The first goal of this paper is to provide an introduction to the methods available, with discussion at both a practical and also a nontechnical theoretical level, including comparison of methods. The second goal is to provide access to the literature, especially on smoothing parameter selection, but ...

We suggest a biased-bootstrap method for monotonising general linear, kernel-type estimators, for example local linear estimators and Nadaraya-Watson estimators. Attributes of our approach include the fact that it produces smooth estimates, that is applicable to a particularly wide range of estimator types, and that it can be employed after the smoothing step has been implemented. Therefore , a...

where X(k) = (X(k)1, . . . , X(k)d), and X(k) is the k-th nearest neighbor of x when points are ordered by increasing values of the product ∏d j=1 |xj−X(k)j |, and k = o(log n), k → ∞. The auxiliary results needed permit us to formulate universal consistency results (pointwise and in L1) for product kernel estimates with different window widths for each coordinate, and for rectangular partition...

We consider kernel density estimation when the observations are contaminated by measurement errors. It is well known that the success of kernel estimators depends heavily on the choice of a smoothing parameter called the bandwidth. A number of data-driven bandwidth selectors exist in the literature, but they are all global. Such techniques are appropriate when the density is relatively simple, ...

Abstract Composite spatial data on administrative area level are often presented by maps. The aim is to detect regional differences in the concentration of subpopulations, like elderly persons, ethnic minorities, low-educated voters a political party or persons with certain disease. Thematic collections such maps different atlases. standard presentation Choropleth where each unit represented si...

Recent studies suggest that the minimum error entropy (MEE) criterion can outperform the traditional mean square error criterion in supervised machine learning, especially in nonlinear and non-Gaussian situations. In practice, however, one has to estimate the error entropy from the samples since in general the analytical evaluation of error entropy is not possible. By the Parzen windowing appro...