Point Estimation and MLE
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چکیده
♦ parameter space-Ω = {all θ} ♦ estimator-a random variable (or vector) ♦ estimate-a value (vector) derived from a realization ♦ (log)-likelihood function-n i=1 f (x i ; θ). ♦ maximum likelihood estimator (estimate)[mle]) is called an unbiased estimator of θ. Otherwise, it is said to be biased. ♦ parameter estimation by method of moments. Example 1: mle for the mean and variance of a random sample of size n from N(θ 1 , θ 2). Example 2: mle for the mean of a random sample of size n from an exponential distribution with a mean α > 0.
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