Regression analysis: likelihood, error and entropy

• Published in: Mathematical programming Vol. 174; no. 1-2; pp. 145 - 166
• Main Authors: Grechuk, Bogdan, Zabarankin, Michael
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2019; Springer Nature B.V
• Subjects: Calculus of Variations and Optimal Control; Optimization; Combinatorics; Empirical analysis; Entropy; Entropy of solution; Error analysis; Estimators; Finance; Full Length Paper; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Maximization; Normal distribution; Norms; Numerical Analysis; Probability density functions; Random variables; Regression analysis; Robustness (mathematics); Statistical analysis; Theoretical; estimator; 90C25; Likelihood; Regression; 90C90; Entropy; 90C15; Error measure

In a regression with independent and identically distributed normal residuals, the log-likelihood function yields an empirical form of the L 2 -norm, whereas the normal distribution can be obtained as a solution of differential entropy maximization subject to a constraint on the L 2 -norm of a rando...