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By Forman S. Acton

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That is, if the observation W, is uncensored, its realized value wJis equal to c,, whereas if it is censored at c J , then w,is some value greater than cJ ( j = 1, . . n) . In this example, the unknown parameter vector 9 is a scalar, being equal to p. We suppose now that the observations have been relabeled so that W1, . . , W, denote the T uncensored observations and WT+l, . . , W , the ri - r censored observations. The log likelihood function for p formed on the basis of y is given by n logL(p) = -7-logp- c c , / p .

N) . In this example, the unknown parameter vector 9 is a scalar, being equal to p. We suppose now that the observations have been relabeled so that W1, . . , W, denote the T uncensored observations and WT+l, . . , W , the ri - r censored observations. The log likelihood function for p formed on the basis of y is given by n logL(p) = -7-logp- c c , / p . But in this simple case, it is instructive to demonstrate how the EM algorithm would work. FORMULATION OF THE EM ALGORITHM The complete-data vector 2 21 can be declared to be 2 ..

One of the roots is negative, and so it is the other root that we seek. Although the likelihood equation can be solved explicitly to find the MLE 6 of 9, we shall use this example to illustrate the computation of the MLE via Newton-type methods and the EM algorithm. In a later section we shall give an example of a multinomial depending on two unknown parameters where the likelihood equation cannot be solved explicitly. 14) in Figure 1 . 1 will cause difficulty with these methods. 0357 (see Thisted, 1988, page 176).

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