![Sample our Economics, Finance,Business & Industry journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5931/TOC-Subject-Sample-2021-Economics-Finance-Business-Industry.jpg"})
Abstract
For specified functions φ and ψ and unknown distribution function F with density f, the efficacy-related parameter T(f) = ∫ φ(x)ψ(F(x))f
2(x)dx may be estimated by the sample analogue estimator T(fn
) based on an empirical density estimator fn
. For {Xi
} i.i.d. F and fn
of the form fn
(x) = n
-1
, we approximate the estimation error T(fn
) - T(f) by the Gateaux derivative of the functional T(·) at the “point” f with increment fn
-f. In conjunction with stochastic properties of the L
2-norm ‖fn
-f‖, this approach leads to characterizations of the stochastic behavior of T(fn
)-T(f). In particular, under mild assumptions on f, we obtain the rate of strong convergence T(fn
)-T(f)=a.s.
O(n-1/2(log n)1/2), which significantly improves previous results in the literature. Also, we establish asymptotic normality with associated Berry-Esséen rates.