Discrete M-robust designs for regression models

• Published in: Journal of statistical planning and inference Vol. 131; no. 2; pp. 393 - 406
• Main Authors: Tsai, Yu-Ling, Zhou, Julie
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.05.2005; New York,NY Elsevier Science; Amsterdam
• Subjects: Annealing algorithm; Change of bias function; Change of variance function; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Discrete design; Exact sciences and technology; Experimental design; General topics; Linear inference, regression; Mathematics; Moving average process; Penalty function; Probability and statistics; Sciences and techniques of general use; Statistics; 62M10; Moving average process; Penalty function; primary 62K05; Change of bias function; Change of variance function; Annealing algorithm; 62F35; secondary 62J05; Discrete design; Error estimation; Bias; Estimator robustness; Linear model; Variance; Simulated annealing; 62M10 Annealing algorithm; Linear regression; Misspecified model; Statistical decision; Algorithm; Mean estimation; Statistical method; Statistical regression; Regression model; Experimental design; Mean error; Autocorrelation; Biased estimation
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2003.09.038

M-robust designs are defined and constructed for misspecified linear regression models with possibly autocorrelated errors on a discrete design space. These designs minimize the mean-squared errors if linear regression models are correct with uncorrelated errors, subject to two robust constraints which control the change of the bias and the change of variance under model departures. Simulated annealing algorithm is applied to construct M-robust designs. Examples are given to show M-robust designs and compare them with minimax robust designs.