Optimal Designs for Rational Function Regression

DOI10.1080/01621459.2012.656035zbMath1261.62072arXiv1009.1444OpenAlexW2170721105MaRDI QIDQ4916472

David Papp

Publication date: 22 April 2013

Published in: Journal of the American Statistical Association (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1444

zbMATH Keywords

Semidefinite programmingExperimental designPositive polynomials

Mathematics Subject Classification ID

Related Items (24)

Optimal Design of Experiments for Implicit Models ⋮ An algorithm based on semidefinite programming for finding minimax optimal designs ⋮ R-optimal designs for multi-response regression models with multi-factors ⋮ Computing exact \(D\)-optimal designs by mixed integer second-order cone programming ⋮ A faster interior-point method for sum-of-squares optimization ⋮ Minimax A‐, c‐, and I‐optimal regression designs for models with heteroscedastic errors ⋮ Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming‐Based Approach ⋮ Semi-Infinite Programming using High-Degree Polynomial Interpolants and Semidefinite Programming ⋮ The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices ⋮ Adaptive grid semidefinite programming for finding optimal designs ⋮ On the semidefinite representation of real functions applied to symmetric matrices ⋮ New optimal design criteria for regression models with asymmetric errors ⋮ Sum-of-Squares Optimization without Semidefinite Programming ⋮ Approximate optimal designs for multivariate polynomial regression ⋮ D-optimal designs based on the second-order least squares estimator ⋮ Using SeDuMi to find various optimal designs for regression models ⋮ Optimal experimental design for linear time invariant state-space models ⋮ Optimal design of multifactor experiments via grid exploration ⋮ Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming ⋮ Computing D-Optimal Experimental Designs for Estimating Treatment Contrasts Under the Presence of a Nuisance Time Trend ⋮ Minimax robust designs for regression models with heteroscedastic errors ⋮ K-Optimal Design via Semidefinite Programming and Entropy Optimization ⋮ Computing A-optimal and E-optimal designs for regression models via semidefinite programming ⋮ A semi-infinite programming based algorithm for finding minimax optimal designs for nonlinear models

Uses Software

• CVX
• YALMIP

Cites Work

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• Optimal design of multi-response experiments using semi-definite programming
• On minimally-supported \(D\)-optimal designs for polynomial regression with log-concave weight function
• \(E\)-optimal designs for polynomial regression without intercept
• Optimal designs for a class of polynomials of odd or even degree
• How bad are Hankel matrices?
• \(D\)-optimal designs for polynomial regression models through origin
• \(E\)-optimal designs for rational models
• Determination of the inertia of a partitioned Hermitian matrix
• Lectures on Modern Convex Optimization
• The Spacing of Observations in Polynomial Regression
• Efficiency Problems in Polynomial Estimation
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• Semidefinite Programming
• GloptiPoly
• Convex Analysis
• Spacing of Information in Polynomial Regression

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