ABSTRACT
Usingm,arealizationofthemaximumlikelihoodestimatorM,onecanestimate Q(q;tt)atqby
g(q;m)=m[q+(l-q)log(l-q))
andcalculateitsstandarderrorS£[g(q;m)]bysubstitutingmfortt0toget m[q+(l-q)log(l-q)]
S£[g(q;m)]=.JN
Notethatintheexponentialcase,theLCisinvarianttotheparameterflsince
Q(q)Q(q) L(q;tt)=£[Y]=--;,:- =[q+(l-q)log(l-q)]
sonoestimationisrequired. Intheothertwoexamples,theLCsandGLCsarenonlinearfunctionsofthe
parameters.Wefinditusefultoconsidertheseexamplesfurther,sincetheyillustrate welltheclassoftechnicalproblemsfacedbyresearchers.IntheParetocase,where
theGLCsolves
Now
sotheLCis
BecauseQ(q;e0,e1)and£(q;e,)arecontinuousfunctionsofeoande1,themaximumlikelihoodestimatorsofthemare