Optimal model selection in density estimation
Matthieu Lerasle (IMT)
TL;DR
This paper introduces penalized least-squares estimators for density estimation using the slope heuristic and resampling penalties, providing theoretical guarantees and practical comparisons.
Contribution
It develops new model selection methods with proven oracle inequalities and evaluates their performance through simulations.
Findings
Oracle inequalities with leading constant asymptotically equal to 1
Resampling penalties perform well in practice
Methods outperform traditional approaches in simulations
Abstract
We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to 1. We compare the practical performances of these methods in a short simulation study.
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Taxonomy
TopicsStatistical Methods and Inference · Advanced Statistical Methods and Models · Bayesian Methods and Mixture Models