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Asymptotic Statistics by A.W. van der Vaart

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25

Semiparametric Models

           This chapter is concerned with statistical models that are indexed by infinite-dimensional parameters. It gives an introduction to the theory of asymptotic efficiency, and discusses methods of estimation and testing.

25.1 Introduction

Semiparametric models are statistical models in which the parameter is not a Euclidean vector but ranges over an “infinite-dimensional” parameter set. A different name is “model with a large parameter space.” In the situation in which the observations consist of a random sample from a common distribution P, the model is simply the set image of all possible values of P: a collection of ...

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