Principe d'invariance sur le processus de vraisemblance (Q790525)

An invariance principle is established for the likelihood process in the regular model. To be specific, consider a sequence \(X_ 1,X_ 2,..\). of i.i.d. random variables. For \(n\geq 1\), \(m\geq 1\) and 0\(\leq t\leq 1\), define \(Z_ n(m,t)=\exp \{mn^{-frac{1}{2}}\sum X_ i-(nt-[nt])X_{[nt]+1}- m^ 2t/2\},\) where [x] is the integer part of x and the sum runs from \(i=1\) to [nt]. Then conditions which guarantee the weak convergence of \(Z_ n(m,t)\) as \(n\to \infty\) are presented.