The asymptotic properties of the least squares estimator of the cusp in some nonlinear nonregular regression models is investigated via the study of the weak convergence of the least squares process generalizing earlier results in Prakasa Rao ( Statist. Prob. Lett. 3 (1985), 15-18).

Approaches for meaningful regressor construction in the linear prediction problem are investigated in a framework similar to partial least squares and continuum regression, but weighted to allow for intelligent specification of an evaluative scheme. A cross-validatory continuum regression procedure is proposed, and shown to compare well with ordinary continuum regression in empirical demonstrat...

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This paper is concerned with regression under a “sum” of partial order constraints. Examples include locally monotonic, piecewise monotonic, runlength constrained, and unimodal and oligomodal regression. These are of interest not only in nonlinear filtering but also in density estimation and chromatographic analysis. It is shown that under a least absolute error criterion, these problems can be...

The focus is on robust regression methods for problems where the predictor matrix has full rank and where it is rank deficient. For the first situation, various robust regression methods have been introduced, and here an overview of the most important proposals is given. For the latter case, robust partial least squares regression is discussed. The way of downweighting outlying observations is ...

A nonlinear regression model with correlated, normally distributed errors is investigated. The bias and the mean square error matrix of the approximate least squares estimator of regression parameters are derived and their limit properties are studied.

| This paper is concerned with regression under a \sum" of partial order constraints. Examples include locally monotonic, piecewise monotonic, runlength constrained, and uni-and oligo-modal regression. These are of interest in nonlinear ltering, but also in density estimation and chromatographic analysis. It is shown that, under a least absolute error criterion, these problems can be transforme...

A nonlinear regression model with correlated, normally distributed errors with non zero means is investigated. The limit properties of bias and the mean square error matrix of the approximate least squares estimator of regression parameters are studied.