S231 Lecture 4 Cyntha

# It determines how much more or less consistent the

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Unformatted text preview: less consistent the data is with the parameter 1 versus 2 . L( 1 )/L( 2 ) is also unaected if we multiply L( ) by a constant so n n we can drop the term (y ) in (y ) y (1 )n y and de...ne L( ) = y (1 )n y . Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 20 / 45 If you' a likelihood value, (relative) size matters: re The shape of L( ) and its maximum value are not aected if we multiply L( ) by a constant. Relative value at two dierent values of the parameter, e.g. L( 1 )/L( 2 ) is important. It determines how much more or less consistent the data is with the parameter 1 versus 2 . L( 1 )/L( 2 ) is also unaected if we multiply L( ) by a constant so n n we can drop the term (y ) in (y ) y (1 )n y and de...ne L( ) = y (1 )n y . n ^ Both (y ) y (1 )n y and y (1 )n y are maximized at = y /n and have the same shape. Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 20 / 45 The Relative Likelihood Function De...nition The Relative likelihood function is R ( ) = L( ) for 2 . ^ L( ) R ( ) has a maximum value equal to one. ^ Log likelihood function: `( ) = log L( ) for 2 . Note that also maximizes `( ). Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 21 / 45 The Relative Likelihood Function De...nition The Relative likelihood function is R ( ) = L( ) for 2 . ^ L( ) R ( ) has a maximum value equal to one. ^ Log likelihood function: `( ) = log L( ) for 2 . Note that also maximizes `( ). ^ Log relative likelihood function: log R ( ) for 2 . Note that also maximizes this. Statistics and Actuarial Science () Model Fitting, Estimation and Checking Jan 2013 21 / 45 The Relative Likelihood Function De...nition The Relative likelihood function is R ( ) = L( ) for 2 . ^ L( ) R ( ) has a maximum value equal to one. ^ Log likelihood function: `( ) = log L( ) for 2 . Note that also maximizes `( ). ^ Log relative likelihood function: log R ( ) for 2 . Note that also maximizes this. d`...
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## This note was uploaded on 04/17/2013 for the course STAT 231 taught by Professor Cantremember during the Winter '08 term at Waterloo.

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