Related papers: Optimal Designs for Regression on Lie Groups

Locally optimal designs for generalized linear models are derived at certain values of the regression parameters. In the present paper a general setup of the generalized linear model is considered. Analytic solutions for optimal designs are…

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to…

This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class…

We identify a class of left-invariant pseudo-Riemannian metrics on Lie groups for which the Laplace-Beltrami equation reduces to a first-order PDE and admits exact solutions. The defining condition is the existence of a commutative ideal…

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…

The subject of this work is two treatment groups random coefficient regression models, in which observational units receive some group-specific treatments. We provide A- and D-optimality criteria for the estimation of the fixed parameter…

Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the…

This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of…

In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…

Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…

In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…

We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets.…

The problem of constructing optimal discriminating designs for a class of regression models is considered. We investigate a version of the $T_p$-optimality criterion as introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 289-303]. The…

We consider optimal designs for the Kiefer cirteria, which include the E-criterion as a particular case, and the G-criterion in random coefficients regression (RCR) models. We obtain general the Kiefer criteria for approximate designs and…

We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…

Under the Neyman causal model, it is well-known that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to…

We study the task of training regression models with the guarantee of label differential privacy (DP). Based on a global prior distribution on label values, which could be obtained privately, we derive a label DP randomization mechanism…

The subject of this work is multiple group random coefficients regression models with several treatments and one control group. Such models are often used for studies with cluster randomized trials. We investigate A-, D- and E-optimal…

We show that the $A$-optimal design optimization problem over $m$ design points in $\mathbb{R}^n$ is equivalent to minimizing a quadratic function plus a group lasso sparsity inducing term over $n\times m$ real matrices. This observation…