(i) Let Pi have density pi with respect to a dominating measure Show that P1 P01 defined by p1 p0 d is independent of the choice of and is a metric (ii) Show the Hellinger distance defined in (15 12) is also independent of and is a metri ...

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(i). Let Pi have density pi with respect to a dominating measure . Show that P1 ...

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(i). Let Pi have density pi with respect to a dominating measure μ.

Show that P1 − P01 defined by |p1 − p0|dμ is independent of the choice of μ

and is a metric.

(ii). Show the Hellinger distance defined in (15.12) is also independent of μ and is a metri

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Testing Statistical Hypotheses Volume I

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

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(i). Let Pi have density pi with respect to a dominating measure . Show that P1 ...

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