Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T06:55:20.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Central Limit Theorems for Dependent Heterogeneous Random Variables

Published online by Cambridge University Press:  11 February 2009

Robert M. de Jong
Robert M. de Jong
Affiliation:
Tilburg University
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents central limit theorems for triangular arrays of mixingale and near-epoch-dependent random variables. The central limit theorem for near-epoch-dependent random variables improves results from the literature in various respects. The approach is to define a suitable Bernstein blocking scheme and apply a martingale difference central limit theorem, which in combination with weak dependence conditions renders the result. The most important application of this central limit theorem is the improvement of the conditions that have to be imposed for asymptotic normality of minimization estimators.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 3 , June 1997 , pp. 353 - 367
Copyright
Copyright © Cambridge University Press 1997

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

Andrews, D.W.K. (1988) Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory 4, 458–467.CrossRefGoogle Scholar
Bernstein, S. (1927) Sur l'extension du theoreme du calcul des probability aux sommes de quantity dependantes. Mathematische Annalen 97, 1–59.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. New York: Wiley.Google Scholar
Davidson, J. (1992) A central limit theorem for globally nonstationary near-epoch dependent functions of mixing processes. Econometric Theory 8, 313–334.CrossRefGoogle Scholar
Davidson, J. (1993) The central limit theorem for globally nonstationary near-epoch dependent functions of mixing processes: The asymptotically degenerate case. Econometric Theory 9, 402–412.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford: Oxford University Press.CrossRefGoogle Scholar
Davidson, J. & de Jong, R.M. (1995) Strong Laws of Large Numbers for Dependent Heterogeneous Processes: A Synthesis of New Results. Working paper, Tilburg University.Google Scholar
Doukhan, P., Massart, P., & Rio, E. (1994) The functional central limit theorem for strongly mixing processes. Annales de I'Institute Henri Poincari, Probability et Statistiques 10, 63–82.Google Scholar
Gallant, A.R. & White, H. (1988) A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models. New York: Basil Black well.Google Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Applications. New York: Academic Press.Google Scholar
Hansen, B.E. (1991) Strong laws for dependent heterogeneous processes. Econometric Theory 7, 213–221.CrossRefGoogle Scholar
Hansen, B.E. (1992) Strong laws for dependent heterogeneous processes. Erratum. Econometric Theory 8, 421–422.Google Scholar
Herrndorf, N. (1984) A functional central limit theorem for weakly dependent sequences of dependent random variables. Annals of Probability 12, 141–153.CrossRefGoogle Scholar
McLeish, D.L. (1975a) A maximal inequality and dependent strong laws. Annals of Probability 3, 829–839.CrossRefGoogle Scholar
McLeish, D.L. (1975b) Invariance principles for dependent variables. Zeitschrift fur Wahrscheinlichskeitstheorie und Verwandte Cebiete 33, 165–178.CrossRefGoogle Scholar
McLeish, D.L. (1977) On the invariance principle for nonstationary mixingales. Annals of Probability 5, 616–621.CrossRefGoogle Scholar
Potscher, B.M. & Prucha, I.R. (1991a) Basic structure of the asymptotic theory in dynamic nonlinear econometric models, part 1: Consistency and approximation concepts. Econometric Reviews 10, 125–216.CrossRefGoogle Scholar
Potscher, B.M. & Prucha, I.R. (1991b) Basic structure of the asymptotic theory in dynamic nonlinear econometric models, part 2: Asymptotic normality. Econometric Reviews 10, 253–325.Google Scholar
Whithers, C.S. (1981) Central limit theorems for dependent variables. Zeitschrift fur fVahrscheinlichkeitstheorie und Verwandte Cebiete 57, 509–534.CrossRefGoogle Scholar
Wooldridge, J.M. & White, H. (1988) Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometric Theory 4, 210–230.CrossRefGoogle Scholar