Transcription of Maximum Likelihood Estimation - University of Washington
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Maximum Likelihood EstimationEric ZivotMay 14, 2001 This version: November 15, 20091 Maximum Likelihood The Likelihood FunctionLetX1,..,Xnbe an iid sample with probability density function (pdf)f(xi; ),where is a(k 1)vector of parameters that characterizef(xi; ).For example, ifXi N( , 2)thenf(xi; )=(2 2) 1/2exp( 12 2(xi )2)and =( , 2) densityof the sample is, by independence, equal to the product of the marginaldensitiesf(x1,..,xn; )=f(x1; ) f(xn; )=nYi=1f(xi; ).The joint density is anndimensional function of the datax1.
Maximum Likelihood Estimation Eric Zivot May 14, 2001 This version: November 15, 2009 1 Maximum Likelihood Estimation 1.1 The Likelihood Function Let X1,...,Xn be an iid sample with probability density function (pdf) f(xi;θ), where θis a (k× 1) vector of parameters that characterize f(xi;θ).For example, if Xi˜N(μ,σ2) then f(xi;θ)=(2πσ2)−1/2 exp(−1
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