STAT 135 Lecture 8: MLE properties
Properties
1Equivalence property of me
Thm :if Ernie is an MLE of aand 9is afunction Cnot necessarily
monotonic )then QCEMLE )Is an MLE of 9ha )
X~Ber (a)
Find mle of varcxkoa -o)
We Know Em #=X
varcx )= 967=-04-0 )✓
=>MLE of varcx )is OCFE)me =Emi (I-Emu)
y=gco7=o Cto )
fcl ,o)44 -
M
,1f1
!Ijgco )Yz I-0
!tdefine ←Max
IYou -0 )likcu )=suplliklo ))
'14 -0
Egtu )
⇒§mi= 0
2consistency
§mL €-0
We require
a) Data xi - - 'xn identically distributed
b) parameter ais interior point in parameter space
c) logco)is differentiable
d) Eis aunique Max of lteko
