On adaptive estimation based on ranks in ARMA processes

• Autorzy: Allali J. , Kaaouachi A. , Melhaoui S.
• Języki publikacji: EN

Abstrakty

EN

This paper describes the adaptive estimation problem based on ranks for the parameter of an ARMA process. The local asymptotic normality property with a ranked based central sequence allows for the construction of estimators which are locally asymptotically minimax (LAM). By using a consistent estimate of the score function, we obtain the adaptive estimators which are LAM and which do not depend on the innovation density.

Słowa kluczowe

EN

local asymptotic normality; LAN; asymptotic linearity; locally asymptotically minimax; LAM; adaptivity

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 2
• Strony: 293--302
• Opis fizyczny: Biblogr. 16 poz.

Twórcy

autor

Allali J.

• Département de Mathématiques, Faculté des Sciences, Université Mohamed Premier Oujda, 60000 Morocco

autor

Kaaouachi A.

• Département de Mathématiques, Faculté des Sciences, Université Mohamed Premier Oujda, 60000 Morocco

autor

Melhaoui S.

• Département de Mathématiques, Faculté des Sciences, Université Mohamed Premier Oujda, 60000 Morocco

Bibliografia

• [1] J. Allal, A. Kaaouachi and D. Paindaveine, R-estimationfor ARMA models, Journal of Nonparametric Statistics 13 (2001), pp. 815-831.
• [2] P. J. Bickel, On adaptive estimation, Ann. Statist. 10 (1982), pp. 647-671.
• [3] P. J. Bickel, C. A. J. Klaassen, Y. Ritov and J. A. Wellner, Efficient and Adaptive Statistical Inference for Semiparametric Models, Johns Hopkins University Press, Baltimore 1993.
• [4] F. G. Drost, C. A. J. Klaassen and B. J. M. Werker, Adaptive estimation in time-series models, Ann. Statist. 25 (1997), pp. 786-817.
• [5] V. Fabian and J. Hannan, On estimation and adaptive estimation for locally asymptotically normal families, Z. Wahrsch. verw. Gebiete 59 (1982), pp. 459-478.
• [6] W. A. Fuller, Introduction to Statistical Time Series, 2nd ed., Wiley, New York 1976.
• [7] J. Hájek and Z. Šidák, Theory of Rank Tests, Academic Press, New York 1967.
• [8] M. Hall in and M. L. Puri, Aligned rank tests for linear models with autocorrelated error terms, J. Multivariate Anal. 50 (1994), pp. 175-237.
• [9] P. Jeganathan, Some aspects of asymptotic theory with applications to time series models, Econometric Theory 11 (1995), pp. 818-887.
• [10] B. K. Kim and J. Van Ryzin, Estimation of the derivative of a density and related functions, Comm. Statist. Theory Methods A 9 (7) (1985), pp. 697-709.
• [11] H. L, Koul and A. Schick, Efficient estimation in nonlinear autoregressive time series models, Bernoulli 3 (1997), pp. 247-277.
• [12] J. P. Kreiss, On adaptive estimation in stationary ARMA processes, Ann. Statist. 15 (1987), pp. 112-133.
• [13] J. P. Kreiss, On adaptive estimation in autoregressive models when there are nuisance functions, Statist. Decisions 5 (1987), pp. 59-76.
• [14] L. Le Cam, Locally asymptotically normal families of distributions, Univ. Calif. Publ. Statist. 3 (I960), pp. 37-98.
• [15] C. Stein, Efficient nonparametric testing and estimation, Proc. Third Berkeley Sympos. Math. Statist, and Probab. (Univ. Calif. Press) I (1956), pp. 187-195.
• [16] C. J. Stone, Adaptive maximum likelihood estimators of a location parameter, Ann. Statist. 3 (1975), pp. 267-284.