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Large sample behavior of entropy measures when parameters are estimated |
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| Authors: | L Pardo D Morales M Salicrú ML Menéndez |
| Institution: | 1. Dep. Estadistica e I.O. Fac. Matemálicas , Univ. Complutense de Madrid , MADRID, 28040, SPAIN;2. Dep. Estadística e I.O. Fac. Matemáticas , Univ. Complutense Madrid , MADRID, 28040, SPAIN;3. Dep. Estadística , Univ. Barcelona , Av. Diagonal, 645, BARCELONA, 08028, SPAIN;4. Dep. Matemática Aplicada E.T.S. Arquitectura , Univ. Politécnica Madrid , MADRID, 20049, SPAIN |
| Abstract: | In this paper, we study the asymptotic behavior of (h,π)-entropy statistics when the parameters are replaced by some consistent and asymptotically normal (CAN) estimates. In the case of stratified sampling, asymptotic distribution is obtained and the optimum allocation is derived for a fixed cost and for a fixed variance. Some tests of hypotheses are constructed on the basis of these asymptotic distributions and a numerical example is presented. |
| Keywords: | Entropy measures CAN estimators Asymptotic distribution random sampling stratified random sampling |