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Pré-Publication, Document De Travail Année : 2014

A general procedure to combine estimators

Résumé

We propose a general method to combine several estimators of the same quantity in order to produce a better estimate. In the spirit of model and forecast averaging, the final estimator is computed as a weighted average of the initial ones, where the weights are constrained to sum to one. In this framework, the optimal weights, minimizing the quadratic loss, are entirely determined by the mean square error matrix of the vector of initial estimators. The averaging estimator is derived using an estimation of this matrix, which can be computed from the same dataset. We prove a non-asymptotic error bound on the averaging estimator and we show that it is asymptotically optimal under mild conditions on the estimated mean square error matrix. This method is illustrated on standard statistical problems in parametric and semi-parametric models where the averaging estimator outperforms the initial estimators in most cases.
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Dates et versions

hal-00936024 , version 1 (24-01-2014)
hal-00936024 , version 2 (25-04-2014)
hal-00936024 , version 3 (03-10-2014)
hal-00936024 , version 4 (12-03-2015)

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Frédéric Lavancier, Paul Rochet. A general procedure to combine estimators. 2014. ⟨hal-00936024v3⟩
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