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An overview of shape-constrained estimation problems

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If you have a question about this talk, please contact Elena Yudovina.

Shape-constrained density estimation has received a great deal of interest recently. The allure is the prospect of obtaining fully automatic nonparametric estimators with no tuning parameters. The general idea dates back to Grenander (1956), who derived the maximum likelihood estimator of a decreasing density on [0,∞). Some other popular shape-constraints include convex and log-concave.

In this talk, I will give a brief overview of the area, focusing particularly on the log-concave constraint (i.e. the logarithm of the density function is concave). I will also mention nice applications of this technique in regression problems and time series analysis. Essential background of nonparametric statistics will also be covered with R demonstrations.

This talk is part of the Statistical Laboratory Graduate Seminars series.

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