To= min(Y1, ... , YN]

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