Related papers: Minimax Robust Designs for M-Estimated Models

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…

This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…

In experimental design, we are given a large collection of vectors, each with a hidden response value that we assume derives from an underlying linear model, and we wish to pick a small subset of the vectors such that querying the…

For experiments running in field plots or over time, the observations are often correlated due to spatial or serial correlation, which leads to correlated errors in a linear model analyzing the treatment means. Without knowing the exact…

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,…

In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we…

In this article, we investigate the robust optimal design problem for the prediction of response when the fitted regression models are only approximately specified, and observations might be missing completely at random. The intuitive idea…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

We discuss, and give examples of, methods for randomly implementing some minimax robust designs from the literature. These have the advantage, over their deterministic counterparts, of having bounded maximum loss in large and very rich…

The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…

We consider minimax-optimal designs for the prediction of individual parameters in random coefficient regression models. We focus on the minimax-criterion, which minimizes the "worst case" for the basic criterion with respect to the…

Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they…

In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes…

Many existing methods for constructing optimal split-plot designs, such as D-optimal designs, only focus on minimizing the variances and covariances of the estimation for the fitted model. However, the underlying true model is usually…

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…

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in…

We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…

In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…

Randomized experiments are the gold standard for estimating the causal effects of an intervention. In the simplest setting, each experimental unit is randomly assigned to receive treatment or control, and then the outcomes in each treatment…

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…