Squared error-based shrinkage estimators of discrete probabilities and their application to variable selection

Małgorzata Łazȩcka () and Jan Mielniczuk ()
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Małgorzata Łazȩcka: Warsaw University of Technology
Jan Mielniczuk: Warsaw University of Technology

Statistical Papers, 2023, vol. 64, issue 1, No 3, 72 pages

Abstract: Abstract In the paper we consider a new approach to regularize the maximum likelihood estimator of a discrete probability distribution and its application in variable selection. The method relies on choosing a parameter of its convex combination with a low-dimensional target distribution by minimising the squared error (SE) instead of the mean SE (MSE). The choice of an optimal parameter for every sample results in not larger MSE than MSE for James–Stein shrinkage estimator of discrete probability distribution. The introduced parameter is estimated by cross-validation and is shown to perform promisingly for synthetic dependence models. The method is applied to introduce regularized versions of information based variable selection criteria which are investigated in numerical experiments and turn out to work better than commonly used plug-in estimators under several scenarios.

Keywords: Discrete distribution; Shrinkage estimator; Stochastic measure of accuracy; Regularisation parameter; Conditional mutual information; Variable selection; Crossvalidation; Squared error; Gini index (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01308-w

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