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Smoothed log-concave maximum likelihood estimation with applications
Classification Functional estimation Log-concave maximum likelihood estimation Log-concavity Smoothing
2011/3/18
We study the smoothed log-concave maximum likelihood estimator of a probability distribution on $\mathbb{R}^d$. This is a fully automatic nonparametric density estimator, obtained as a canonical smoot...
Inference and Modeling with Log-concave Distributions
Nonparametric density estimation shape constraint log-concave density Polya frequency function
2010/10/14
Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions ...
Approximation by Log-Concave Distributions with Applications to Regression
Convex support isotonic regression linear regression Mallows’ distance projection
2010/3/10
We study the approximation of arbitrary distributions P on d-dimensional space by distributions
with log-concave density. Approximation means minimizing a Kullback–Leibler type functional.
We show t...
Active Set and EM Algorithms for Log-Concave Densities Based on Complete and Censored Data
Active Set EM Algorithms Log-Concave Densities Complete and Censored Data
2010/4/30
We develop an active set algorithm for the maximum likelihood estimation of a
log–concave density based on complete data. Building on this fast algorithm, we introduce an EM algorithm to treat arbitr...