The subject of Nonparametric statistics is statistical inference applied to noisy observations of infinite-dimensional “parameters” like images and time-dependent signals. This is a mathematical area on the border between Statistics and Functional Analysis, the latter name taken in its “literal” meaning – as geometry of spaces of functions. What follows is the 8-lecture course given by the auth...

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being designed and analyzed, both for the unidimensional and the multivariate setting. In this short ...

This article is concerned with the analysis of recurrent events in the presence of a terminal event such as death. We consider the mean frequency function, defined as the marginal mean of the cumulative number of recurrent events over time. A simple nonparametric estimator for this quantity is presented. It is shown that the estimator, properly normalized, converges weakly to a zero-mean Gaussi...

Kim, J., and Gleser, L. J. (2000), “SIMEX Approaches to Measurement Error in ROC Studies,” Communications in Statistics. Theory and Methods, 29, 2473–2491. Kulathinal, S. B., Kuulasmaa, K., and Gasbarra, D. (2002), “Estimation of an Errors-in-Variables Regression Model When the Variances of the Measurement Errors Vary Between the Observations,” Statistics in Medicine, 21, 1089–1101. Li, T., and...

BACKGROUND Mortality for children with congenital heart disease (CHD) has declined with improved surgical techniques and neonatal screening; however, as these patients live longer, accurate estimates of the prevalence of adults with CHD are lacking. METHODS To determine the prevalence and mortality trends of adults with CHD, we combined National Vital Statistics System data and National Healt...

We consider nonparametric regression estimation for finite population totals for two-stage sampling, in which complete auxiliary information is available for first-stage sampling units. The estimators, based on local polynomial regression, are linear combinations of cluster total estimators, with weights that are calibrated to known control totals. The estimators are asymptotically design-unbia...