3 research outputs found
Sparse Density Estimation with Measurement Errors
This paper aims to build an estimate of an unknown density of the data with
measurement error as a linear combination of functions from a dictionary.
Inspired by the penalization approach, we propose the weighted Elastic-net
penalized minimal -distance method for sparse coefficients estimation,
where the adaptive weights come from sharp concentration inequalities. The
optimal weighted tuning parameters are obtained by the first-order conditions
holding with a high probability. Under local coherence or minimal eigenvalue
assumptions, non-asymptotical oracle inequalities are derived. These
theoretical results are transposed to obtain the support recovery with a high
probability. Then, some numerical experiments for discrete and continuous
distributions confirm the significant improvement obtained by our procedure
when compared with other conventional approaches. Finally, the application is
performed in a meteorology data set. It shows that our method has potency and
superiority of detecting the shape of multi-mode density compared with other
conventional approaches.Comment: 34 pages, 4 figure
Sparse Density Estimation with Measurement Errors
This paper aims to estimate an unknown density of the data with measurement errors as a linear combination of functions from a dictionary. The main novelty is the proposal and investigation of the corrected sparse density estimator (CSDE). Inspired by the penalization approach, we propose the weighted Elastic-net penalized minimal ℓ2-distance method for sparse coefficients estimation, where the adaptive weights come from sharp concentration inequalities. The first-order conditions holding a high probability obtain the optimal weighted tuning parameters. Under local coherence or minimal eigenvalue assumptions, non-asymptotic oracle inequalities are derived. These theoretical results are transposed to obtain the support recovery with a high probability. Some numerical experiments for discrete and continuous distributions confirm the significant improvement obtained by our procedure when compared with other conventional approaches. Finally, the application is performed in a meteorology dataset. It shows that our method has potency and superiority in detecting multi-mode density shapes compared with other conventional approaches