Abstract
Le Cam’s first lemma is of fundamental importance to modern theory of statistical inference: it is a key result in the foundation of the Convolution Theorem, which implies a very general form of the optimality of the maximum likelihood estimate and any statistic that is asymptotically equivalent to it. This lemma is also important for developing asymptotically efficient tests. In this note we give a relatively simple but detailed proof of Le Cam’s first lemma. Our proof allows us to grasp the central idea by making analogies between contiguity and absolute continuity, and is particularly attractive when teaching this lemma in a classroom setting.
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Acknowledgments
G. Jogesh Babu thanks the Statistical and Applied Mathematical Sciences Institute (SAMSI), for supporting his research during his visit to SAMSI in Fall 2019. This material was based upon work partially supported by the National Science Foundation under Grant DMS-1638521 to the Statistical and Applied Mathematical Sciences Institute. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Bing Li’s work is partially supported by the National Science Foundation Grant DMS-1713078.
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Babu, G.J., Li, B. A Revisit to Le Cam’s First Lemma. Sankhya A 83, 597–606 (2021). https://doi.org/10.1007/s13171-020-00223-2
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DOI: https://doi.org/10.1007/s13171-020-00223-2