We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that the tests are consistent against general...

In the paper we propose nonparametric approaches for elearning data. In particular we want to supply a measure of the relative exercises importance, to estimate the acquired Knowledge for each student and finally to personalize the e-learning platform. The methodology employed is based on a comparison between nonparametric statistics for kernel density classification and parametric models such ...

One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the regression function is to be estimated. The number of observations ‘local’ to the point of estimation decreases exponentially with the number of dime...

Title of Dissertation: Nonparametric Quasi-likelihood in Longitudinal Data Analysis Xiaoping Jiang, Doctor of Philosophy, 2004 Dissertation directed by: Professor Paul J. Smith Statistics Program Department of Mathematics This dissertation proposes a nonparametric quasi-likelihood approach to estimate regression coefficients in the class of generalized linear regression models for longitudinal ...

Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. A Phase II nonparametric CUSUM chart based on the exceedance statistics, called the exceedance CUSUM chart, is proposed here for detecting a shift in the unknown location parameter of a continuous distribution. The exceedance statistics can be more efficient ...

Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153–193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. We extend their work to the...

This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals. These models belong to the difficult (nonlinear) ill-posed inverse problems with unknown operators, and include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. For these models it is generally difficult to verify wh...

Changepoints have been extensively analysed in order to identify structural changes in time series data, typically when the data are of known parametric form. This report presents an exploration of methods to detect changepoints in a nonparametric setting, where no assumptions are made with regard to the distributional structure of the data, yet must still maintain a specified level of performa...

Simulations that generate very large data sets in one and many dimensions are increasingly common. Nonparametric density estimates based on these data sets are often required and estimators that can be generated and manipulated efficiently are needed. In computer graphics, for example, nonparametric density estimates over surfaces can be used to represent lighting functions [1]. These simulatio...

This study develops practical methods for Bayesian nonparametric inference in regression models. The emphasis is on extending a nonparametric treatment of the regression function to the full conditional distribution. It applies these methods to the relationship of earnings of men in the United States to their age and education over the period 1967 through 1996. Principal findings include increa...