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• W2024554257 abstract "We consider the problem of estimating the conditional density π of a response vector Y given the predictor X (which is assumed to be a continuous variable). We provide an adaptive nonparametric strategy to estimate π based on model selection.We start with a collection of finite-dimensional product spaces spanned by orthonormal bases. But instead of expanding directly the target function π on these bases, we prefer to consider the expansion of h(x, y) = π(F −1(x),y), where F is the cumulative distribution function of X. This ‘warping’ of the bases allows us to propose a family of projection estimators easier to compute than estimators resulting from the minimization of a regression-type contrast. The data-driven selection of the best estimator ĥ for the function h is done with a model selection device in the spirit of Goldenshluger and Lepski (2011). The resulting estimator is $bar pi (x,y) = hat h(hat F(x),y)$ , where $hat F$ is the empirical distribution function. We prove that it realises a global squared bias/variance compromise, in the context of anisotropic function classes: we establish non-asymptotic mean-squared integrated risk bounds and also provide risk convergence rates. Simulation experiments illustrate the method." @default.
• W2024554257 created "2016-06-24" @default.
• W2024554257 creator A5086695528 @default.
• W2024554257 date "2013-10-01" @default.
• W2024554257 modified "2023-10-16" @default.
• W2024554257 title "Warped bases for conditional density estimation" @default.
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• W2024554257 doi "https://doi.org/10.3103/s1066530713040017" @default.
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