approach enables us to construct new estimators and, most importantly, to propose an automatic selection method for an unknown parameter on which all the existing non-parametric estimators of A(·) depend. Constrained smoothing splines and convex hull techniques are used to force the obtained estimators

We explain some basic theoretical issues regarding nonparametric statistics applied to inverse problems. Simple examples are used to present classical concepts such as the white noise model, risk estimation, minimax risk, model selection and optimal rates of convergence, as well as more recent

Abstract. In this tutorial paper we give an overview of deconvolution problems in nonparametric statistics. First, we consider the problem of density estimation given a contaminated sample. We illustrate that the classical Rosenblatt-Parzen kernel density estimator is unable to capture the full

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of pairs of neurons or neuronal groups (the multiple comparisons problem). We show that nonparametric statistical tests provide con-vincing and elegant solutions for both problems. We also show that these tests allow to incorporate biophysically motivated constraints in the test statistic, which may

This is a survey of problems and recent developments ~n some selected areas of nonparametric statistical theory. The paper is divided into three parts, Nonparametric versus parametric tests, Robust estimates, and Robust analysis of variance. SOMMAIRE Ce travail est une revue des probl~mes et des d

Abstract The ruin probability of an insurance company is a central topic in risk theory. In this paper, the classical Poisson risk model is considered and a nonparametric estimator of the ruin probability is provided. Strong consistency and asymptotic normality of the estimator are estabilished

Abstract. Many nonparametric estimators and tests are naturally set in infinite dimensional contexts. Prevalence is the infinite dimensional analogue of full Lebesgue measure, shyness the analogue of being a Lebesgue null set. A prevalent set of prior distributions lead to wildly inconsistent

A number of X2 based nonparametric tests are used to determine the level of statistical significance. Once the significance level is determined with X21 Cramer's V can be used to measure the strength of association. Values for the maximum possible Xz are given for six nonparametric tests

but ignored. This article reviews the current practice and then theoretically and empirically examines several suitable tests. Based on that, we recommend a set of simple, yet safe and robust non-parametric tests for statistical comparisons of classifiers: the Wilcoxon signed ranks test for comparison of two