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Asymptotic distributions of least squares estimators of the coefficients in the model of linear regression with nonlinear constraints and long-memory dependence
Author(s):
E.
M.
Moldavs'ka
Translated by:
O. I. Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 75
(2006).
Journal:
Theor. Probability and Math. Statist.
No. 75
(2007),
121-137.
MSC (2000):
Primary 62E20, 62F10;
Secondary 60G18
Posted:
January 24, 2008
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Additional information
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:
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):
23/OCT/2004
Posted:
January 24, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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