ABSTRACT
The method of maximum likelihood is appealing because, as we have said, in some sense a maximum-likelihood estimate is the most plausible parameter value after an observation x has been made – it is that value of the parameter which gives greatest probability to x. However while we may accept this, we should be extremely reluctant to believe that a maximum-likelihood estimate coincided with the true parameter in all circumstances, and it is natural to ask how near the true parameter we might expect a maximum-likelihood estimate (or indeed any estimate) to be. The very use of the phrase ‘how near’ implies that there is a metric on the parameter space, but it is useful to think about this question in more general terms.
