worksheet12

worksheet12 - pdf, their joint pdf is Q n i =1 f ( x i ; )....

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Stat 400 In Class Worksheet 12 T.A. Emily King April 30, 2008 Goal : Find a point estimator ˆ θ for a quantity θ , given a random sample X 1 , X 2 , . . . X n from a pdf. Method 1 : Method of Moments Step 1 : Find a formula for θ in terms of E ( X ) , E ( X 2 ) , E ( X 3 ) , etc. Note : Recall that V ( X ) = E ( X 2 ) - [ E ( X )] 2 . Step 2 : Replace each E ( X k ) in the formula that you found in Step 1 with 1 n n i =1 X k i . When k = 1, this is simply X this is your formula for the point estimator ˆ θ . Step 3 : Given values from a random sample, x 1 , x 2 , . . . , x n , plug in the values to find the point estimate. Method 2 : Maximum Likelihood Estimator (MLE) The pdf is of the form f ( x ; θ ). Step 1 : Since X 1 , X 2 , . . . X n are independent readings from the same
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Unformatted text preview: pdf, their joint pdf is Q n i =1 f ( x i ; ). This is the likelihood function. Step 2 : We want to maximize the likelihood function with respect to . This is usually accomplished by maximized the loglikelihood function (because the algebra and calculus necessary to solve the problem are easier). Step 3 : The value of which maximizes the (log)likelihood function is the MLE . Step 4 : Given values from a random sample, x 1 , x 2 , . . . , x n , plug in the values to nd the point estimate....
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