AMDA-2008-Session 8 - Hypothesis Testing and P-values II...

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Unformatted text preview: Hypothesis Testing and P-values II Likelihood Ratio Test 1 to restricted is when mle the is and mle the is where ) ( ) ( ln 2 ) ( sup ) ( sup ln 2 is statistic ratio likelihood The : H versus : H esting Consider t = = L L L L Likelihood Ratio Test . of value observed the is where ) P( is test for the value- p The . of dimension the minus of dimension the is q- r where ~ ) ,..., ( , : H Under statistic. ratio likelihood the be Let )}. ,..., ( ) ,..., ( : { Let ). ,..., , ,..., ( that Suppose 2 q- r 2 1 , 1 , 1 1 1 = = =- + + + q r a n r q r q r q q X X Let X 1 ,,X n be iid N(,1). Find the LRT for H : =0 versus H 1 : 0 Let X 1 ,,X n be iid N(,). Find the LRT for H : (,)=(0,1) versus H 1 :(,) (0,1) Let X 1 ,,X n be iid Ber(p). Find the LRT be iid Ber(p)....
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AMDA-2008-Session 8 - Hypothesis Testing and P-values II...

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