arXiv subjects

Douglas P. Wiens

Publications and source records attributed to Douglas P. Wiens.

5 recordsLinked to original sources

arXiv2026

Minimax Robust Designs for M-Estimated Models

Experimental designs that are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. The theory to date has focussed almost exclusively on Least Squares estimates. Here we extend this theory to designs tailored for M-estimation of parameters, thus obtaining additional robustness against outlying responses. We show that, subject to a minor change in a tuning constant, designs optimal for Least Squares remain so asymptotically for M-estimation. We argue that even this minor change should be ignored, and the tuning constant chosen in an ad hoc but sensible manner which does not depend on which M-estimate is being employed. A rather surprising additional result is that our designs and estimates, derived under an assumption of i.i.d. errors, are also robust, in a minimax sense, against broad classes of correlation structures.

math.ST↗

arXiv2026

Minimum Variance Designs With Constrained Maximum Bias

Designs which are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. This mean squared error decomposes into a term arising solely from variation, and a bias term arising from the model errors. Here we consider the problem of designing so as to minimize the variance of the predictors, subject to a bound on the maximum (over model misspecifications) bias. We consider as well designing so as to minimize the maximum bias, subject to a bound on the variance. We show that solutions to both problems are given by the minimax designs, with appropriately chosen values of their tuning constants. Conversely, any minimax design solves each problem for an appropriate choice of the bound on the maximum bias or on the variance.

math.ST↗

arXiv2025

To ignore dependencies is perhaps not a sin

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. In a statistical context in which such functions measure loss, this says that the least favourable form of dependence is in fact independence, so that a procedure optimal for i.i.d.\ data can be minimax. In particular, the ordinary least squares (\textsc{ols}) estimate of a correctly specified regression response is minimax among generalized least squares (\textsc{gls}) estimates, when the maximum is taken over certain classes of error covariance structures and the loss function possesses a natural monotonicity property. An implication is that it can be not only safe, but optimal to ignore such departures from the usual assumption of i.i.d.\ errors. We then consider regression models in which the response function is possibly misspecified, and show that \textsc{ols} is minimax if the design is uniform on its support, but that this often fails otherwise. We go on to investigate the interplay between minimax \textsc{gls} procedures and minimax designs, leading us to extend, to robustness against dependencies, an existing observation -- that robustness against model misspecifications is increased by splitting replicates into clusters of observations at nearby locations.

math.ST↗

arXiv2024

A Note on Minimax Robustness of Designs Against Correlated or Heteroscedastic Responses

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment.

math.ST↗

arXiv2014

Model-Robust Designs for Quantile Regression

We give methods for the construction of designs for linear models, when the purpose of the investigation is the estimation of the conditional quantile function and the estimation method is quantile regression. The designs are robust against misspecified response functions, and against unanticipated heteroscedasticity. The methods are illustrated by example, and in a case study in which they are applied to growth charts.

stat.ME↗