Estimation of a matrix-valued parameter of an autoregressive process with nonstationary noise

Authors:
A. P. Yurachkivskii and D. O. Ivanenko

Translated by:
V. Zayats

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **72** (2005).

Journal:
Theor. Probability and Math. Statist. **72** (2006), 177-191

MSC (2000):
Primary 62F12; Secondary 60F05

DOI:
https://doi.org/10.1090/S0094-9000-06-00675-2

Published electronically:
September 6, 2006

MathSciNet review:
2168147

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that is the least squares estimator constructed from observations of an unknown matrix in an autoregressive process . Under the assumption that the sequence is a martingale difference, not necessarily stationary and ergodic, we find the limit distribution as of the statistic by using methods of stochastic analysis. This limit distribution may be different from the normal distribution.

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Additional Information

**A. P. Yurachkivskii**

Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty of Radiophysics, Taras Shevchenko National University, Glushkov Ave. 2, Building 5, 03127 Kyïv, Ukraine

Email:
yap@univ.kiev.ua

**D. O. Ivanenko**

Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty of Radiophysics, Taras Shevchenko National University, Glushkov Ave. 2, Building 5, 03127 Kyïv, Ukraine

Email:
ida@univ.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-06-00675-2

Received by editor(s):
May 24, 2004

Published electronically:
September 6, 2006

Article copyright:
© Copyright 2006
American Mathematical Society