A Revisit to Le Cam’s First Lemma

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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Work Title A Revisit to Le Cam’s First Lemma
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Open Access
Creators
  1. G. Jogesh Babu
  2. Bing Li
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Sankhya A: The Indian Journal of Statistics
Publication Date November 17, 2020
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/s13171-020-00223-2.
Deposited July 19, 2022

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    Work Title
    • A revisit to le cam’s first lemma
    • A Revisit to Le Cam’s First Lemma
    Publisher
    • Sankhya: The Indian Journal of Statistics
    • Sankhya A: The Indian Journal of Statistics
    Description
    • <p>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 analo-gies between contiguity and absolute continuity, and is particularly attractive when teaching this lemma in a classroom setting.</p>
    • <p>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.</p>
    Publication Date
    • 2021-01-01
    • 2020-11-17
  • Updated