Department of Statistics
University of California, Berkeley
“Accuracy of Maximum Likelihood Estimators in Shape Constrained Estimation”
Shape constrained estimation is a subfield of nonparametric estimation where one seeks to estimate the unknown object of interest (such as a regression function or a density) under natural shape constraints such as monotonicity, convexity, concavity, log-concavity etc. The estimator of choice in these problems is usually the maximum likelihood estimator (MLE). This talk will aim to shed some light on the accuracy of the MLE in these problems under natural global loss functions. I will focus on the interesting way in which the accuracy of the MLE changes with the underlying unknown parameter value.