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Fisher's Method of Maximum Likelihood is shown to be a procedure for theconstruction of likelihood intervals or regions, instead of a procedure ofpoint estimation. Based on Fisher's articles and books it is justified that byestimation Fisher meant the construction of likelihood intervals or regionsfrom appropriate likelihood function and that an estimate is a statistic, thatis, a function from a sample space to a parameter space such that thelikelihood function obtained from the sampling distribution of the statistic atthe observed value of the statistic is used to construct likelihood intervalsor regions. Thus Problem of Estimation is how to choose the 'best' estimate.Fisher's solution for the problem of estimation is Maximum Likelihood Estimate(MLE). Fisher's Theory of Statistical Estimation is a chain of ideas used tojustify MLE as the solution of the problem of estimation. The construction ofconfidence intervals by the delta method from the asymptotic normaldistribution of MLE is based on Fisher's ideas, but is against his 'logic ofstatistical inference'. Instead the construction of confidence intervals fromthe profile likelihood function of a given interest function of the parametervector is considered as a solution more in line with Fisher's 'ideology'. A newmethod of calculation of profile likelihood-based confidence intervals forgeneral smooth interest functions in general statistical models is considered.

What Did Fisher Mean by An Estimate?