Let X1,..., Xn be i.i.d. P on S. Suppose S is countable and let E be the

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Let X1,..., Xn be i.i.d. P on S. Suppose S is countable and let E be the collection of all subsets of S. Let Pˆ

n be the empirical measure; that is, for any subset E of E, Pˆ

n(E) is the proportion of observations Xi that fall in E. Prove, with probability one, sup E∈E

|Pˆ

n(E) − P(E)| → 0 .

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Testing Statistical Hypotheses Volume I

ISBN: 9783030705770

4th Edition

Authors: E.L. Lehmann, Joseph P. Romano

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Question Posted: Nov 04, 2024 04:00 AM

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Let X1,..., Xn be i.i.d. P on S. Suppose S is countable and let E be the

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Testing Statistical Hypotheses Volume I

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