Density estimation with heteroscedastic error

By Aurore Delaigle, A. Meister. 2008

88 citations recorded by the source corpus.

veloped for homoscedastic errors become inconsistent. In this paper, we introduce a kernel estimator of a density in the case of heteroscedastic contamination. We establish consistency of the estimator and show that it achieves optimal rates of convergence under quite general conditions. We study the limits of appli cation of the procedure in some extreme situations, where we show that, in some cases, our estimator is consistent, even when the scaling parameter of the error is unbounded. We suggest a modified estimator for the problem where the distribution of the errors is unknown, but replicated observations are available. Finally, an adaptive procedure for selecting the smoothing parameter is proposed and its finite-sample prop erties are investigated on simulated examples.

Subfields: Artificial Intelligence, Computer Networks and Communications, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d0ce6cd74b275afb5a36e0ad8e1c2713de7ce2ba

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Citations in the corpus

Identifying distributional characteristics in random coefficients panel data models (2009, background): “and E [Hi (θ) (yi − a(Wi; θ)) |Wi] = E (γi|Wi) , (28)”
Extreme deconvolution: Inferring complete distribution functions from noisy, heterogeneous and incomplete observations (2009, background): “etric techniques that assume that the noise is homoskedastic [e.g., Stefanski and Carroll (1990); Zhang (1990)]. The case of heteroskedastic uncertainties has only recently attracted attention [e.g., Delaigle and Meister (2008); Staudenmayer, Ruppert and Buonaccorsi (2008)], and all of the approache”