Let X1, , Xn be an observed random sample and X(n1 1), ,Xn be the missing (at random) observations Assume that Xi are iid from an N(, 2) distribution (a) Show that are sufficient statistics for y (, 2) (b) Obtain the EM sequence for y (, 2) (c) Consider a censored normal sample with n 10, with the largest three being censored Gupta Using the results of part (a), obtain an EM estimate of y (, 2) with an arbitrary starting point 1613 644 1 663 1 732 1 740 1 763 1 778

Question: Let X1, . . ., Xn be an observed random sample and X(n1 + 1), . . . ,Xn be the missing (at random) observations.

Let X1, . . ., Xn be an observed random sample and X(n1 + 1), . . . ,Xn be the missing (at random) observations. Assume that Xi are iid from an N(Î¼, Ïƒ2) distribution.
(a) Show that

are sufficient statistics for y = (Î¼, Ïƒ2).
(b) Obtain the EM sequence for y = (Î¼, Ïƒ2).
(c) Consider a censored normal sample with n = 10, with the largest three being censored [Gupta].

Using the results of part (a), obtain an EM estimate of y = (Î¼, Ïƒ2) with an arbitrary starting point.

1613 .644 1.663 1.732 1.740 1.763 1.778

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