The strengths and weaknesses of L2 approximable regressors

Mynbaev, Kairat (2001): The strengths and weaknesses of L2 approximable regressors. Published in: Two Essays on Econometrics. Fortaleza: Expressão Gráfica , Vol. 1, (2001): pp. 1-20.

Abstract

The most part of the paper is about modeling (or approximating) nonstochastic regressors. Examples of regressors which are (not) L2-approximable are given. Applications to central limit theory and OLS estimator asymptotics are provided.

• Item Type: MPRA Paper
• Language: English
• Keywords: L2-approximable regressors; linear regression; OLS estimator; central limit theorem; asymptotic theory
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods

References

Anderson, T. W. (1971) The Statistical Analysis of Times Series. Wiley and Sons. New York.

Bai, J., R. L. Lumsdaine and J. H. Stock (1998) Testing for and Dating Common Breaks in Multivariate Time Series. Review of Economic Studies, 65, 395-432.

Canjels, E. and M. W. Watson (1997) Estimating Deterministic Trends in the Presence of Serially Correlated Errors. Review of Economics and Statistics. 79, 184-200.

Davidson, J. (1994) Stochastic Limit Theory. Oxford: Oxford University Press.

Grenander, U. and M. Rosenblatt (1957) Statistical Analysis of Stationary Time Series. New York. Chelsea Publishing Company.

Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press. Princeton, New Jersey.

Kato, T. (1966) Perturbation Theory for Linear Operators. New York: Springer – Verlag.

Milbrodt, H. (1992) Testing Stationarity in the Mean of Autoregressive Processes with a Nonparametric Regression Trend. Ann. Statist. 20, N.º 3, 1426-1440.

Millar, P. W. (1982) Optimal Estimation of a General Regression Function. Ann. Statist. 10, 717-740.

Moussatat, M. W. (1976) On the Asymptotic Theory of Statistical Experiments and Some of Its Applications. Ph.D. dissertation, Univ. California, Berkeley.

Mynbaev, K. T. (1997) Linear Models with Regressors Generated by Square-Integrable Functions. Programa e Resumos, 7 Escola de Séries Temporais e Econometria. 6 a 8 de agosto, 80-82.

Mynbaev, K. T. (2000) Limits of Weighted Sums of Random Variables. Discussion Text. Economics Dept. Federal University of Ceará, Fortaleza, Brazil. 20pp.

Mynbaev, K. T. and A. Lemos (to be published). Econometria. Um Guia Conciso da Teoria Clássica. Editora da Fundação Getúlio Vargas, Rio de Janeiro, RJ.

Sims, C. A., J. H. Stock, M. W. Watson (1990) Inference in Linear Time Series Models with Some Unit Roots. Econometrica, 58, N.º 1, 113-144.

Srinivasan, C. and M. Zhou (1995) A Central Limit Theorem for Weighted and Integrated Martingales. Scand. J. Statist. 22, 493-504.

Vogelsang, T. J. (1998) Trend Function Hypothesis Testing in the Presence of Serial Correlation. Econometrica 66, N.º 1, 123-148.

Yoshihara, Ken-ichi (1997a) Central Limit Theorems for Weighted D[0, 1]-Valued Mixing Sequences. I. Functional Central Limit Theorems for Weighted Sums. Proceedings of the Second World Congress of Nonlinear Analysts, Part 6, (Athens, 1966). Nonlinear Analysis, 30, No. 6, 3569-3573.

Yoshihara, Ken-ichi (1997b) Central Limit Theorems for Weighted D[0, 1]-Valued Mixing Sequences. II. Functional Central Limit Theorems for Integrated Variables. Yokohama Math. J. 44, N.º 2, 157-167.