Limit theorems for Phi-divergences based on k-spacings and its applications

• Autores: Raúl Jiménez
• Localización: XXXI Congreso Nacional de Estadística e Investigación Operativa ; V Jornadas de Estadística Pública: Murcia, 10-13 de febrero de 2009 : Libro de Actas, 2009, ISBN 978-84-691-8159-1
• Idioma: inglés
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• Resumen

  • 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.