S231 Lecture 4 Cyntha

It determines how much more or less consistent the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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`...
View Full Document

This note was uploaded on 04/17/2013 for the course STAT 231 taught by Professor Cantremember during the Winter '08 term at Waterloo.

Ask a homework question - tutors are online