Consider the choice of values for aML and bML for the purpose of maximizing ln L(1, 2,
Question:
Consider the choice of values for aML and bML for the purpose of maximizing ln L(εâ•›1, εâ•›2, . . . , εn) in equation (15.55). Usually, this would require us to differentiate the log-likelihood with respect to these estimates. In this case, however, we can make the choice by drawing on previous results.
(a) Only the last term in equation (15.55) contains aML and bML. What is the sign on the summation in which they appear?
(b) What is the sign on the term in which this summation appears?
(c) Given parts a and
b, what must our choices of aML and bML accomplish with regard to the value of the summation in which they appear if we are to maximize the log-likelihood?
(d) How does this summation compare to the sum of squared errors in chapter 4?
(e) What does this comparison indicate about the validity of the assertions that aML = a and bML = b?
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