Smoothed log-concave maximum likelihood estimation with applications

By Yining Chen, Richard J. Samworth. 2011

54 citations recorded by the source corpus.

We study the smoothed log-concave maximum likelihood estimator of a probability distribution on R d . This is a fully automatic nonparametric density estimator, obtained as a canonical smoothing of the log-concave maximum likelihood estimator. We demonstrate its attractive features both through an analysis of its theoretical properties and a simulation study. Moreover, we show how the estimator can be used as an intermediate stage of more involved procedures, such as constructing a classifier or estimating a functional of the density. Here again, the use of the estimator can be justified both on theoretical grounds and through its finite sample performance, and we illustrate its use in a breast cancer diagnosis (classification) problem.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a86bce61d2b14bc54bb384089898a94332d03fda

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Global rates of convergence in log-concave density estimation (2014, methodology): “, 2011), Independent Component Analysis (Samworth and Yuan, 2012) and classification (Chen and Samworth, 2013). However, statistical procedures based on log-concavity, in common with other methods based on shape constraints, present substantial computational and theoretical challenges and these have”
Generalized additive and index models with shape constraints (2014, background): “…certain other shape-constrained estimation problems where boundary effects are also observed, such as log-concave density estimation, it is possible to construct a fully automatic smoothed estimate to alleviate these issues (Dümbgen and Rufibach, 2009; Cule et al., 2010; Chen and Samworth, 2013).”
Count Time Series: A Methodological Review (2021, result): “This approach is similar in spirit to that in Chen and Samworth (2013) for continuousvalued series, where the noise distribution is assumed to be log-concave.”
Recent Progress in Log-Concave Density Estimation (2017, background): “A different proof of this fact was given in Chen and Samworth (2013), Theorem 5.”