MLE估計相關的問題
以下兩個MLE的問題想請教, 感謝:
a. In likelihood theory, impossible observations have probability 0 and therefore log probability of –∞ and never happen, i.e. 0 times. The sum of the log likelihood of those impossible observations is therefore 0 times –∞. This causes no difficulty in likelihood theory. Why not?
想法:If the observations are impossible, they won't be observed by definition. Therefore, they have nothing to do with the calculation of the likelihood which uses the observations values.
b. On the other hand, one single impossible observation in the data set destroys maximum likelihood, no matter how large the sample is. Why?
想法: the parameters assumed to be true cannot be true in the first place.
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