2022
DOI: 10.1214/22-ejs2037
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Minimax optimal conditional density estimation under total variation smoothness

Abstract: This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in a multivariate setting. We first demonstrate that conditional density estimation is impossible if one only requires that p X|Z is smooth in x for all values of z. This motivates us to consider a sub-class of absolutely continuous distributions, restricting the conditional density p X|Z (x|z) to not only be Hölder smooth in x, but also be total variation smooth in z. We propose a … Show more

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Cited by 3 publications
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References 27 publications
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