In a nonlinear regression model with a given prior distribution, the estimator maximizing the posterior probability density is considered (a certain kind of Bayes estimator). It is shown that the prior influences essentially, but in a comprehensive way, the geometry of the model, including the intrinsic curvature measure of nonlinearity which is derived in the paper. The obtained geometrical re...

This paper deals with functional regression, in which the input attributes as well as the response are functions. To deal with this problem, we develop a functional reproducing kernel Hilbert space approach; here, a kernel is an operator acting on a function and yielding a function. We demonstrate basic properties of these functional RKHS, as well as a representer theorem for this setting; we i...

We study parameter estimation for sparse nonlinear regression. More specifically, we assume the data are given by y = f(x�β∗) + �, where f is nonlinear. To recover β∗, we propose an �1regularized least-squares estimator. Unlike classical linear regression, the corresponding optimization problem is nonconvex because of the nonlinearity of f . In spite of the nonconvexity, we prove that under mil...

We consider regression when the predictor is measured with error and an instrumental variable is available. The regression function can be modeled linearly, nonlinearly, or nonparametrically. Our major new result shows that the regression function and all parameters in the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identif...

In this contribution, genetic programming is combined with continuum regression to produce two novel nonlinear continuum regression algorithms. The first is a 'sequential' algorithm while the second adopts a 'team-based' strategy. Having discussed continuum regression, the modifications required to extend the algorithm for nonlinear modelling are outlined. The results of two case studies are th...

In the context of nonlinear regression models, this paper outlines recent de­ velopments in design strategies when the assumed model function, initial parameter guesses, and/or error structure are not known with complete certainty. Designs obtained using these strategies are termed robust de­ signs as they are intended to be robust to specified departures. Robust designs are clearly advantageou...

it is necessary to use empirical models for estimating of instantaneous peak discharge because of deficit of gauging stations in the country. hence, at present study, two models including artificial neural networks and nonlinear multivariate regression were used to predict peak discharge in taleghan watershed. maximum daily mean discharge and corresponding daily rainfall, one day antecedent and...