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Classical Theory of Estimation

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A Graduate Course on Statistical Inference

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Abstract

This chapter is a concise description of the classical theory of point estimation, which seeks optimal estimator among the class of all unbiased estimators, in the sense that it has the smallest variance. The optimal problem involved is intrinsically connected with the notions of sufficiency, minimal sufficiency, completeness, Fisher information, and the Cramer-Rao lower bound. An important class of distributions where sufficient and complete statistics are available is the exponential family, which is also covered in this chapter.

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Authors and Affiliations

  1. Department of Statistics, Penn State University, University Park, PA, USA

    Bing Li & G. Jogesh Babu

Authors
  1. Bing Li
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  2. G. Jogesh Babu
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Correspondence to Bing Li .

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Li, B., Babu, G.J. (2019). Classical Theory of Estimation. In: A Graduate Course on Statistical Inference. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9761-9_2

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