Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T07:46:31.357Z Has data issue: false hasContentIssue false
  • English
  • Français

A central limit theorem for systems of regressions*

Published online by Cambridge University Press:  24 October 2008

E. J. Hannan
E. J. Hannan
Affiliation:
The University of North Carolina and School of General StudiesThe Australian National University
Get access Rights & Permissions [Opens in a new window]

Abstract

A central limit theorem is proved for the estimates of the regression coefficients in a multiple system of regressions when the vector process generating the residuals is a linear process with coefficient matrices the sum of whose norms converges. The regressor variables are assumed to satisfy conditions, due to Grenander, which make their generalized harmonic analysis possible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 583 - 588
Copyright
Copyright © Cambridge Philosophical Society 1961

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Anderson, T. W.On asymptotic distributions of estimates of parameters of stochastic difference equations. Ann. Math. Statist. 30 (1959), 676–8.CrossRefGoogle Scholar
(2)Bernstein, S.Sur l'extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes. Math. Ann. 97 (1927), 1–59.CrossRefGoogle Scholar
(3)Cramér, H.Mathematical methods of statistics (Princeton, 1947).Google Scholar
(4)Diananda, P. H.Some probability limit, theorems with statistical applications. Proc. Camb. Phil. Soc. 49 (1953), 239–46.CrossRefGoogle Scholar
(5)Grenander, U.On the estimation of the regression coefficients in the case of an autocorrelated disturbance. Ann. Math. Statist. 25 (1954), 252–72.CrossRefGoogle Scholar
(6)Grenander, U. and Rosenblatt, M.Statistical analysis of stationary time series (New York, 1957).CrossRefGoogle Scholar
(7)Koopmans, T. J. (Editor). Statistical inference in dynamic economic models (New York, 1950).Google Scholar
(8)Mann, H. B. and Wald, A.On the statistical treatment of linear stochastic difference equations. Econometrica, 11 (1943), 173–220.CrossRefGoogle Scholar
(9)Moran, P. A.Some theorems on time series. Biometrika, 34 (1947), 281–91.CrossRefGoogle ScholarPubMed
(10)Rosenblatt, M.On the estimation of regression coefficients of a vector-valued time series with a stationary residual. Ann. Math. Statist. 27 (1956), 99–121.CrossRefGoogle Scholar