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In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, which considers symmetric design spaces we investigate the…

Statistics Theory · Mathematics 2020-09-21 Holger Dette , Viatcheslav B. Melas , Petr Shpilev

In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…

Statistics Theory · Mathematics 2013-03-13 Holger Dette , Andrey Pepelyshev , Anatoly Zhigljavsky

We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…

Optimization and Control · Mathematics 2023-12-05 Denys Shcherbak , Natalya Pya Arnqvist

Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all…

Methodology · Statistics 2025-10-29 Luzia A. Trinca , Steven G. Gilmour

A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in…

Statistics Theory · Mathematics 2016-03-16 Chrystel Feller , Kirsten Schorning , Holger Dette , Georgina Bermann , Björn Bornkamp

This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the…

Statistics Theory · Mathematics 2021-06-17 Ulrike Graßhoff , Heinz Holling , Frank Röttger , Rainer Schwabe

Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…

Methodology · Statistics 2023-09-26 Ksheera Sagar , Jyotishka Datta , Sayantan Banerjee , Anindya Bhadra

We study random designs that minimize the asymptotic variance of a de-biased lasso estimator when a large pool of unlabeled data is available but measuring the corresponding responses is costly. The optimal sampling distribution arises as…

Statistics Theory · Mathematics 2020-10-27 Hamid Eftekhari , Moulinath Banerjee , Ya'acov Ritov

Configuration spaces of many real mechanical systems appear to be manifolds with singularity. A singularity often indicates that geometry of motion may change at the singular point of configuration space. We face conceptual problem…

Analysis of PDEs · Mathematics 2013-12-24 Maria Sorokina

We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared…

Machine Learning · Computer Science 2020-01-22 Akshay Krishnamurthy , Arya Mazumdar , Andrew McGregor , Soumyabrata Pal

We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…

Optimization and Control · Mathematics 2022-04-05 Gehui Xu , Guanpu Chen , Hongsheng Qi

We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems…

Statistics Theory · Mathematics 2017-10-27 Yohann De Castro , Fabrice Gamboa , Didier Henrion , Roxana Hess , Jean-Bernard Lasserre

We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the…

Computation · Statistics 2014-05-29 Alen Alexanderian , Noemi Petra , Georg Stadler , Omar Ghattas

Subsampling is commonly used to overcome computational and economical bottlenecks in the analysis of finite populations and massive datasets. Existing methods are often limited in scope and use optimality criteria (e.g., A-optimality) with…

Statistics Theory · Mathematics 2023-04-07 Henrik Imberg , Marina Axelson-Fisk , Johan Jonasson

Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…

Computation · Statistics 2018-10-09 Yuanzhi Huang , Steven Gilmour , Kalliopi Mylona , Peter Goos

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the…

Optimization and Control · Mathematics 2020-08-14 Anwesh Reddy Gottu Mukkula , Radoslav Paulen

For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev…

Statistics Theory · Mathematics 2007-06-13 Holger Dette , Viatcheslav B. Melas , Andrey Pepelyshev

This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

Optimization and Control · Mathematics 2023-01-13 Emiland Garrabe , Giovanni Russo

Modeling signals as linear combinations of atoms from a dictionary is ubiquitous in modern signal processing. In the finite-dimensional setting, whenever atoms depend nonlinearly upon unknown parameters, the signal model is said to be…

Signal Processing · Electrical Eng. & Systems 2026-05-04 Santos Michelena , Maxime Ferreira Da Costa , José Picheral

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…

Statistics Theory · Mathematics 2007-06-13 Wolfgang Bischoff , Frank Miller