Combining estimators using the same dataset to produce both the experts and the aggregate

Frédéric Lavancier (1) , Paul Rochet (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

Given several estimators of the same quantity, called experts, we propose a way to aggregate them in order to produce a better estimate. The aggregated estimator is simply a linear combination of the experts, with the minimal requirement that the weights sum to one. In this framework, the optimal weights, minimizing the quadratic loss, are entirely determined by the mean square error matrix of the experts. The aggregation estimator is then obtained using an estimation of this matrix, which can be computed from the same dataset. We show that the aggregate satisfies a non-asymptotic oracle inequality and is asymptotically optimal, provided the mean square error matrix is suitably estimated. This method is illustrated on standard statistical problems: estimation of the position of a symmetric distribution, estimation in a parametric model, density estimation. In most situations, the aggregate outperforms the initial estimators.

Mots clés: Averaging; Aggregation; Oracle inequality; Parametric estimation; Weibull model; Kernel density estimation

Domaines: Méthodologie [stat.ME]

Frédéric Lavancier, Paul Rochet. Combining estimators using the same dataset to produce both the experts and the aggregate. 2014. ⟨hal-00936024v1⟩