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Article Dans Une Revue Electronic Journal of Statistics Année : 2023

Should we estimate a product of density functions by a product of estimators ?

Fabienne Comte
Céline Duval
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Résumé

In this paper, we consider the inverse problem of estimating the product f g of two densities, given a n-sample of i.i.d. observations drawn from each. We propose both projection estimators with model selection device and kernel estimators with bandwidth selection strategies. The procedures do not consist in making the product of each density estimator, but in plugging an overfitted estimator of one of the two densities, in an estimator based on the second sample. Our findings are a first step toward a better understanding of the good performances of overfitting in regression Nadaraya-Watson estimator.
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Dates et versions

hal-03602694 , version 1 (09-03-2022)
hal-03602694 , version 2 (12-10-2022)

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Citer

Fabienne Comte, Céline Duval. Should we estimate a product of density functions by a product of estimators ?. Electronic Journal of Statistics , 2023, 17 (1), pp.198-242. ⟨10.1214/23-EJS2103⟩. ⟨hal-03602694v2⟩
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