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From Estimation to Optimization via Shrinkage

Danial Davarnia (ddavarni***at***andrew.cmu.edu)
Gerard Cornuejols (gc0v***at***andrew.cmu.edu)

Abstract: We study a class of quadratic stochastic programs where the distribution of random variables has unknown parameters. A traditional approach is to estimate the parameters using a maximum likelihood estimator (MLE) and to use this as input in the optimization problem. For the unconstrained case, we show that an estimator that “shrinks” the MLE towards an arbitrary vector yields a uniformly better risk than the MLE. In contrast, when there are constraints, we show that the MLE is admissible.

Keywords: Stochastic optimization, Parameter estimation, Maximum likelihood estimator, Admissible estimator, Shrinkage estimator

Category 1: Stochastic Programming

Category 2: Applications -- Science and Engineering (Statistics )

Category 3: Nonlinear Optimization (Quadratic Programming )

Citation: https://doi.org/10.1016/j.orl.2017.10.005

Download: [PDF]

Entry Submitted: 10/08/2017
Entry Accepted: 10/09/2017
Entry Last Modified: 11/02/2017

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