ABSTRACT
Let MO = {R,F@,O E 8 ) be a parametric statistical model, where R = ( -m, m ) is the sarrlplc spice, 8 is parameter spacc, an opcn subset of' R, and for every H t O, Fe is a probability distribution defined on R. Let s = (xl,. . ; T,,) be a sample of n indeperidcrit idcntically distributed (2.i.d.) observations. The maximum likelihood estimator (rnle)
H,(s) derived from the paran~ctric nlodcl Ado is oftell S;wored by rrimiy statisticiaris for estimating ancl collecting t,hc inforrnat,iori of the ~ m k l ~ o u n parameter H . If the t n ~ e ur~clcrlying tfist,rik)ution (2 = ki is a rncml~cr of the statisticit1 model n;kl (the modcl is correctly specif-ied), then thc rnle has rrmiy large sample optimal properties, for esa.rrrple consis~cncy~ asymptotic normality, a r ~ l exponential ride of convcrgence. The corisistericy of thc n ~ l e has been studied by (ham& (1936), Wald (191!1), LeCarn (1953, 1970), B;thatlirr (1967), and Pfanzagl (1973).
