Estimation and testing under shape constraints

Nilanjana Laha

Over the last few decades, shape constrained methods have increasingly gathered importance in statistical inference as  attractive alternatives to  traditional  nonparametric  methods which often require tuning parameters and restrictive smoothness assumptions. This talk focuses on application of shape-constraints like unimodality and log-concavity in comparing the outcome of two  HIV vaccine trials. To this end, we develop  shape-constrained tests of stochastic dominance, and shape-constrained plug-in estimator of  the Hellinger distance between two densities. Our techniques are either tuning parameter free, or rely on only one tuning parameter, but their performance is comparable with nonparametric methods.   We also show that our tests and estimators have desirable asymptotic properties.

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