
Datadriven aggregation in nonparametric density estimation on the real line
We study nonparametric estimation of an unknown density with support in...
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Adaptive estimation in the linear random coefficients model when regressors have limited variation
We consider a linear model where the coefficientsintercept and slopesa...
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Density Deconvolution with NonStandard Error Distributions: Rates of Convergence and Adaptive Estimation
It is a typical standard assumption in the density deconvolution problem...
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Spectral cutoff regularisation for density estimation under multiplicative measurement errors
We study the nonparametric estimation of an unknown density f with supp...
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Estimation of convex supports from noisy measurements
A popular class of problem in statistics deals with estimating the suppo...
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Anisotropic spectral cutoff estimation under multiplicative measurement errors
We study the nonparametric estimation of an unknown density f with supp...
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Multiplicative deconvolution estimator based on a ridge approach
We study the nonparametric estimation of an unknown density f with supp...
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Datadriven aggregation in circular deconvolution
In a circular deconvolution model we consider the fully data driven density estimation of a circular random variable where the density of the additive independent measurement error is unknown. We have at hand two independent iid samples, one of the contaminated version of the variable of interest, and the other of the additive noise. We show optimality,in an oracle and minimax sense, of a fully datadriven weighted sum of orthogonal series density estimators. Two shapes of random weights are considered, one motivated by a Bayesian approach and the other by a well known model selection method. We derive nonasymptotic upper bounds for the quadratic risk and the maximal quadratic risk over Sobolevlike ellipsoids of the fully datadriven estimator. We compute rates which can be obtained in different configurations for the smoothness of the density of interest and the error density. The rates (strictly) match the optimal oracle or minimax rates for a large variety of cases, and feature otherwise at most a deterioration by a logarithmic factor. We illustrate the performance of the fully datadriven weighted sum of orthogonal series estimators by a simulation study.
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