We consider the problem of learning, from K data, a regression function in a linear space of high dimensionN using projections onto a random subspace of lower dimension M . From any algorithm minimizing the (possibly penalized) empirical risk, we provide bounds on the excess risk of the estimate computed in the projected subspace (compressed domain) in terms of the excess risk of the estimate b...

We introduce a new nonparametric regression estimator that uses prior information on regression shape in the form of a parametric model. In e!ect, we nonparametrically encompass the parametric model. We obtain estimates of the regression function and its derivatives along with local parameter estimates that can be interpreted from within the parametric model. We establish the uniform consistenc...

Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods h...

The behavior of estimators for misspecified parametric models has been well studied. We consider estimators for misspecified nonlinear regression models, with error and covariates possibly dependent. These models are described by specifying a parametric model for the conditional expectation of the response given the covariates. This is a parametric family of conditional constraints, which makes...

chemometric techniques in spectral analysis have gained importance in the quality control of  the drugs mixtures and pharmaceutical formulations containing two or more drugs with overlapping spectra. since theophylline and etophylline have common chromophore, they cannot be analyzed simultaneously using conventional uv methods. simultaneous spectrophotometric determination of etophylline and th...

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bia...