Adaptive Methods for Nonparametric Classification and Regression/Supervised Learning, Inference in HMM and State Space Models and Inference in Semiparametric Models

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In non and semiparametric inference Bickel, in collaboration with Ritov and others, proposes to study how an increasing but proportionally vanishingly small cross validation sample can be used systematically to optimize supervised learning (classification and regression) procedures, for example ADA BOOST. Further they propose to study a unified theory for testing of semiparametric hypotheses and develop efficient tests for bioequivalence. In dependent data models, they propose to extend previous results on Hidden Markov models to state space models and study how procedures obtained by fitting and use of approximate likelihoods such as particle filters behave.The investigator and collaborators propose to analyze and develop new effective methods for identifying (by machine) the type of a newly perceived object or predicting some feature from historical information. This ranges from machine reading of hand written zip codes to predicting travel times of cars from one destination to another to predicting tumor type from microarray data. In a similar direction they propose to see how well computer simulation based approximations to ideal prediction methods work in very complicated models applying to situations such as voice recognition. Further they propose to study methods of inference bearing on questions such as whether a new drug which may be more expensive and have side-effects is sufficiently better than drugs currently in use to be authorized for distribution.