Let X1, , Xn be a random sample from an infinite population with finite variance 2 Define Show that S '2 is a biased estimator for 2, and that the bias of S '2 is 2 n Thus, S '2 is negatively biased, and so on average underestimates the variance Note that S '2 is the MLE of 2 O (, ) ...

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Let X1, . . ., Xn be a random sample from an infinite population with finite variance

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Let X1, . . ., Xn be a random sample from an infinite population with finite variance Ïƒ2. Define

Show that S'2 is a biased estimator for Ïƒ2, and that the bias of S'2 is €“ Ïƒ2 / n. Thus, S'2 is negatively biased, and so on average underestimates the variance. Note that S'2 is the MLE of Ïƒ2.

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Mathematical Statistics With Applications In R

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Authors: Chris P. Tsokos, K.M. Ramachandran

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Question Posted: Nov 23, 2015 03:49 AM

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