ECO220Y5 Study Guide - Final Guide: Maximum Likelihood Estimation, Royal Institute Of Technology, Independent And Identically Distributed Random Variables
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Based on the assumption that the sample moments are good estimates of the corresponding population moments. Ex = is the first population moment is the first sample moment. Ex2 is the second population momentis the second sample moment. Exk is the kth population moment is the kth sample moment. Ex2, etc. is a good estimator of ex = . Sample mean is the moment estimator of the population mean. Estimator will be the value of the parameter that maximizes the likelihood function. Steps: take logarithm, take derivative and equate to 0, solve for parameter. Suppose x1,x2, ,xn is a random sample from a poisson distribution with mean . To estimate parameter of poisson( ) distribution, we recall that 1 = e(x) = . There is only one unknown parameter, hence we write one equation, Solvi(cid:374)g it for , we obtain the method of moments estimator of . , and its logarithm is lnp(x(cid:524) = + xln ln(x!
