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• W2154208473 abstract "This paper deals with the classical statistical problem of comparing the probability distributions of two real random variables $$X$$ and $$X_0$$ , from a double independent sample. While most of the usual tools are based on the cumulative distribution functions $$F$$ and $$F_0$$ of the variables, we focus on the relative density, a function recently used in two-sample problems, and defined as the density of the variable $$F_0(X)$$ . We provide a nonparametric adaptive strategy to estimate the target function. We first define a collection of estimates using a projection on the trigonometric basis and a preliminary estimator of $$F_0$$ . An estimator is selected among this collection of projection estimates, with a criterion in the spirit of the Goldenshluger–Lepski methodology. We show the optimality of the procedure both in the oracle and the minimax sense: the convergence rate for the risk computed from an oracle inequality matches with the lower bound that we also derived. Finally, some simulations illustrate the method." @default.
• W2154208473 created "2016-06-24" @default.
• W2154208473 creator A5039038830 @default.
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• W2154208473 date "2015-01-29" @default.
• W2154208473 modified "2023-09-25" @default.
• W2154208473 title "Optimal adaptive estimation of the relative density" @default.
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• W2154208473 doi "https://doi.org/10.1007/s11749-015-0426-6" @default.
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