Resumen de Limit theorems for Phi-divergences based on k-spacings and its applications
We study the asymptotic behavior of the divergence{based statistic W ;n(G; k) = 1 N XN i=1 ([G(Xik) .. G(X(i..1)k)]N);
where X1 < X2 < : : : < Xn are the order statistics of a random sample of size n, G is a known continuous distribution, is a convex function on (0;+1), k 1 is a xed integer and N the smallest integer greater than or equal to (n+1)=k. Laws of large numbers and central limit theorems for W ;n(G; k) are established under sharp conditions on and an information-type inequality is obtained to characterize the unknown xed distribution which generated the data. Application to goodness{of{ t tests are discussed with respect to general consistency and asymptotic power for several widely used and various k.
