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(μ, σ2) distribution.
(a) Show that

are sufficient statistics for y = (μ, σ2).
(b) Obtain the EM sequence for y = (μ, σ2).
(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 = (μ, σ2) with an arbitrary starting point.

Transcribed Image Text:

1613 .644 1.663 1.732 1.740 1.763 1.778