Maximum-Likelihood Estimation of Linear Regression

Bruce C. Dieffenbach ()
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Bruce C. Dieffenbach: Independent author

Chapter 58 in Conjugate Duality in Economic Analysis, 2026, pp 449-454 from Springer

Abstract: Abstract We perform maximum-likelihood estimation of linear regression by perturbation duality. Transforming the parameters and deploying the quadratic function obtains a maximization concave in the parameters. The reduced dual resembles the standard least-squares linear-regression dual. To carry out a comparative-statics calculation of parameter variances and covariances, adding a choice variable obtains a conjugate maximum-likelihood problem, in which the inner product multiplies the second moments of the data by the parameters. We find the large-sample variances of the parameter estimates via the comparative-statics approach, by calculating how a change in the data affects the estimates. Each sufficient statistic can be varied independently, while holding the others constant.

Date: 2026
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DOI: 10.1007/978-3-032-21396-9_58

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