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Statistica Sinica 11(2001), 863-960



Peter J. Bickel and Jaimyoung Kwon

University of California, Berkeley

Abstract: Non-and semi-parametric models have flourished during the last twenty five years. They have been applied widely and their theoretical properties have been studied extensively. We briefly review some of their development and list a few questions that we would like to see addressed. We develop an answer to one of these questions by formulating a `calculus' similar to that of the i.i.d. case that enables us to analyze the efficiency of procedures in general semiparametric models when a nonparametric model has been defined. Our approach is illustrated by applying it to regression models, counting process models in survival analysis and submodels of Markov chains, which traditionally require elaborate special arguments. In the examples, the calculus lets us easily read off the structure of efficient estimators and check if a candidate estimator is efficient.

Key words and phrases: Asymptotic, efficiency, Markov chains, semiparametric models, survival analysis.

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