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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Asymptotic distributions of least squares estimators of the coefficients in the model of linear regression with nonlinear constraints and long-memory dependence


Author: E. M. Moldavs'ka
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
Journal: Theor. Probability and Math. Statist. 75 (2007), 121-137
MSC (2000): Primary 62E20, 62F10; Secondary 60G18
Published electronically: January 24, 2008
MathSciNet review: 2321186
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Abstract: We consider least squares estimators for linear regression models with long-memory dependence, continuous time, and nonlinear inequality constraints imposed on the parameter. We study the solution of the problem of minimization of the least squares functional in the linear regression with a given (long) radius of dependence and nonlinear inequality constraints imposed on the parameter. We prove that the solution being appropriately centered and normalized converges in distribution to the solution of the quadratic programming problem. The latter solution is non-Gaussian in contrast to known results for long-memory dependence without constraints for which an analogous transform of the solution of the minimization problem is asymptotically Gaussian in many typical cases.


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Additional Information

E. M. Moldavs'ka
Affiliation: Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
Email: elinam@bgu.ac.il

DOI: http://dx.doi.org/10.1090/S0094-9000-08-00719-9
PII: S 0094-9000(08)00719-9
Keywords: Long-memory (strong) dependence, linear regression, least squares estimators, inequality constraints, non-Gaussian distributions, asymptotic distribution, continuous time
Received by editor(s): October 23, 2004
Published electronically: January 24, 2008
Article copyright: © Copyright 2008 American Mathematical Society