Allal, Jelloul and Kaaouachi, Abdelali and Paindaveine, Davy (2001): Restimation for ARMA models. Published in: Journal of Nonparametric Statistics No. 13 (2001): pp. 815831.

PDF
MPRA_paper_21167.pdf Download (207kB)  Preview 
Abstract
This paper is devoted to the Restimation problem for the parameter of a stationary ARMA model. The asymptotic uniform linearity of a suitable vector of rank statistics leads to the asymptotic normality of √nconsistent Restimates resulting from the minimization of the norm of this vector. By using a discretized √nconsistent preliminary estimate, we construct a new class of onestep Restimators. We compute the asymptotic relative efficiency of the proposed estimators with respect to the LS estimator. Efficiency properties are investigated via a MonteCarlo study in the particular case of an AR(1) model.
Item Type:  MPRA Paper 

Original Title:  Restimation for ARMA models 
Language:  English 
Keywords:  Restimation, ARMA models, local asymptotic normality, asymptotic linearity 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General 
Item ID:  21167 
Depositing User:  Davy Paindaveine 
Date Deposited:  07. Mar 2010 04:36 
Last Modified:  10. May 2015 20:15 
References:  Adichie, J.N. (1967). Estimation of regression parameters based on rank tests, Ann. Math. Statist. 38, 894904. Allal, J., (1991). Restimation dans le mod`ele autor ́egressif d’ordre un, Thèse de Doctorat. Université libre de Bruxelles. Chernoff, H. and Savage, I.R., (1958). Asymptotic normality and efficiency of certain nonparamet ric tests. Ann. Math. Statist. 29, 972994. Fuller, W.A., (1976). Introduction to statistical time series, J. Wiley, New York. Ha ́jek, J. and Sˇida ́k, Z., (1967). Theory of rank tests, Academic press, New York. Hallin, M., (1994). On the Pitmannonadmissibility of correlogrambased methods. Journal of Time Series Analysis 15, 607612. Hallin M., Ingenbleek, J.F. and Puri M.L., (1985). Linear serial rank tests for randomness against ARMA alternatives, Ann. Statist. 13, 11561181. Hallin, M. and Puri, M.L., (1994). Aligned rank tests for linear models with autocorrelated error terms, J. Multivariate Anal. 50, 175237. Hodges, J.L. and Lehmann, E.L., (1963). Estimates of location based on rank tests, Ann. Math. Statist. 34, 589611. Jaeckel, L.A., (1972). Estimating regression cœfficients by minimizing the dispersion of the resid uals, Ann. Math. Statist. 43, 14491458. Jureckova, J. (1971). Nonparametric estimate of regression cœfficients, Ann. Math. Statist. 42, 13281338. Jureckova, J. and Sen, P.K. (1996), Robust statistical procedures : asymptotics and interrelations. Koul, H.L., (1971). Asymptotic behavior of a class of confidence regions based on ranks in regression, Ann. Math. Statist. 42, 466476. Koul, H.L. and Saleh, A.K.Md.E., (1993). Restimation of the parameters of autoregressive AR(p) models, Ann. Statist. 21, 534551. Kreiss, J.P., (1987a). On adaptive estimation in stationary ARMA processes, Ann. Statist. 15, 112133. Kreiss, J.P., (1987b). A note on Mestimation in stationary ARMA processes, Statistics and Decisions 3, 317336. Le Cam, L., (1960). Locally asymptotically normal families of distributions. University of California. Publications in Statistics, 3, 3798. Puri, M.L. and Sen, P.R. (1985), Nonparametric methods in general linear models. Yoshihara, K. I. (1976). Limiting behavior of Ustatistics for stationary absolutely regular process, Z. Wahrsch. vew. Gebiete, 35, 237252. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/21167 