Parameter Estimation and Evaluation Maximum Likelihood Estimation Maximum Likelihood Estimation Theorem 1(8.1).[Existence of MLE] Suppose,with probability one,L(X")is a continuous func- tion of0∈曰，and曰is a compact set.Then there exists a global maximizer 0 that solves the problem, =0(X")=arg maxL(x"). -Q Remarks: It is often convenient to solve maxeee In L(X"),where In L(X")is called the log-likelihood function,which is a strictly monotonic increasing function of L(X"). Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21,2020 22207Parameter Estimation and Evaluation Parameter Estimation and Evaluation Introduction to Statistics and Econometrics April 21, 2020 22/207 Maximum Likelihood Estimation Maximum Likelihood Estimation Theorem 1 (8.1). [Existence of MLE] Remarks: