Abstract :
This paper considers a series estimator of E@a~Y!6l~X ! lN #, ~a,l! A L,
indexed by function spaces, and establishes the estimator’s uniform convergence
rate over lN R, a A, and l L, when A and L have a finite integral bracketing
entropy+ The rate of convergence depends on the bracketing entropies of A and L in general+ In particular, we demonstrate that when each l L is locally
uniformly L2-continuous in a parameter from a space of polynomial discrimination
and the basis function vector pK in the series estimator keeps the smallest
eigenvalue of E@ pK~l~X !!pK~l~X !!ʹ # above zero uniformly over l L, we can
obtain the same convergence rate as that established by de Jong ~2002, Journal of
Econometrics 111, 1–9!+
