For the bivariate case it is adapted as follows.
end{aligned} Details of the modulus of continuity for the bivariate case can be found in [25].
The Wooldridge estimator for the bivariate case is estimated as a simulated Maximum Likelihood estimator with 2RN Halton draws.
The same optimization procedure applied for the bivariate case may be applied to construct the MECC for dependence structure in higher dimensions. .
The same optimization procedure applied for the bivariate case may be applied to construct the MECC for dependence structure in higher dimensions.
We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions.
For the bivariate case, the extreme value copula may be written as C u,v) = uvexp left[ {Aleft( {tfrac{log (v)}{log (uv)}} right)} right],, quad u,v in [0,1].
The Clayton copula has a parameter α which is different from the linear correlation parameter, and the relationship between them for the bivariate case is given by: alpha = frac{{{{sin }^{- 1}}({rho_{k}})}}{{pi - 2,{{sin }^{- 1}}({rho_{k}})}}.
The concern of this paper is to obtain Voronoskaja-type asymptotic result by calculating an estimate of fourth order central moment for these operators and discuss the rate of convergence for the bivariate case by using the complete and partial moduli of continuity and the degree of approximation by means of a Lipschitz-type function and the Peetre K-functional.
For (fin C(I^{2})), the complete modulus of continuity for the bivariate case is defined as begin{aligned}& omega(f delta_{1},delta_{2}) & quad = supbigl{ biglvert f t,s -f x,s -f xrvert : (t,y), (x,y) in I^{2}, |t-x|leqdelta_{1}, |s-y|leqdelta_{2} bigrvertnd{aligned} where (delta_{1}, delta_{2}>0).
