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2. use the Jensen's inequality to prove that D(thetaO, theta)>= D(theta0, theta0), where D is defined

2. use the Jensen's inequality to prove that D(thetaO, theta)>= D(theta0, theta0), where D is defined

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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D is defined in the other picture atatched

2. use the Jensen's inequality to prove that D(theta0, theta)>= D(theta0, thetaO), where D is defined
Transcribed Image Text:2. use the Jensen's inequality to prove that D(theta0, theta)>= D(theta0, thetaO), where D is defined
Choose a function p(x, 0), e.g. p(x, 0) = (X - 0)², define D (0o,0) = Ep(X, 0), where the mean is calculated under the distribution X~ Peo- ►Suppose that D(0o,0) measures the discrepancy between 0 and the true value 0 of the parameter in the sense that D(0。,0) is uniquely minimized at 0 = 0. o For example, for the estimate of 0o = E(X), we choose p(x, 0) = (x - 0)2, then D(0o,0) = E. (X – 0)² = S (x - 0) ²dP(x), which is - minimized at 0 = 0 = Eo, (X) = 0o.
Transcribed Image Text:Choose a function p(x, 0), e.g. p(x, 0) = (X - 0)², define D (0o,0) = Ep(X, 0), where the mean is calculated under the distribution X~ Peo- ►Suppose that D(0o,0) measures the discrepancy between 0 and the true value 0 of the parameter in the sense that D(0。,0) is uniquely minimized at 0 = 0. o For example, for the estimate of 0o = E(X), we choose p(x, 0) = (x - 0)2, then D(0o,0) = E. (X – 0)² = S (x - 0) ²dP(x), which is - minimized at 0 = 0 = Eo, (X) = 0o.
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