ABSTRACT
At (asymptotic) probability level a, the Gaussian Lagrange multiplier test then consists in rejecting the null hypothesis R~' 1 (90; 0) (the subscript '!l in R~'J refers to a Gaussian innovation density) whenever the quadratic te~t statistic Q~'J(O("J) exceeds the (1 - n)-quantile
X~- .. :l-o of a chi-square distribution with p-r degrees of freedomthus a typical parametric procedure. However, since Eq. (2.3) holds under any innovation density g E .? ~ {f: Eq. (2.4) holds}, the same test can be performed for the semiparametric null hypothesis H("J(90; 0).
