10.4 The M-Estimators

The method of maximum likelihood is based on the fact that subject to identifiability of the family f,tsi236_e, if X has pdf fx,θsi237_e , then the function Eθlogf(X,t)si238_e has t = θ as its unique maximizer. The MLE of θ based on a random sample X1, …, Xn is the maximizer of n1i=1nlogfXi;tsi239_e which is a natural estimate of Eθlogf(X,t). Equivalently, ...

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