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Convergence systems and strong consistency of least squares estimates in regression models

Author

Listed:
  • Gui-Jing, Chen
  • Lai, T. L.
  • Wei, C. Z.

Abstract

A recent theorem of T. L. Hai, H. Robbins, and C. Z. Wei (J. Multivariate Anal. 9 (1979), 343-362) is extended to a more general form which unifies previous results in the literature on the strong consistency of least squares estimates in multiple regression models with nonrandom regressors. In particular the issue of strong consistency of the least squares estimate in the Gauss-Markov model, in the i.i.d. model with infinite second moment, and in general time series models is examined. In this connection, some basic properties of convergence systems are also obtained and are applied to the strong consistency problem.

Suggested Citation

  • Gui-Jing, Chen & Lai, T. L. & Wei, C. Z., 1981. "Convergence systems and strong consistency of least squares estimates in regression models," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 319-333, September.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:3:p:319-333
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    Citations

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    Cited by:

    1. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.
    2. Marlene MUELLER, "undated". "Consistency properties of model selection criteria in multiple linear regression," Statistic und Oekonometrie 9207, Humboldt Universitaet Berlin.
    3. Wu, Tiee-Jian & Wasan, M. T., 1996. "Weighted least squares estimates in linear regression models for processes with uncorrelated increments," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 273-286, November.
    4. Dzhaparidze, K. & Spreij, P., 1989. "On SLLN for martingales with deterministic variation," Serie Research Memoranda 0079, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    5. Ching-Kang Ing & Ching-Zong Wei, 2005. "A maximal moment inequality for long range dependent time series with applications to estimation and model selection," Econometrics 0508009, University Library of Munich, Germany.
    6. Lita da Silva, João, 2014. "Some strong consistency results in stochastic regression," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 220-226.
    7. Aiting Shen & Yu Zhang & Benqiong Xiao & Andrei Volodin, 2017. "Moment inequalities for m-negatively associated random variables and their applications," Statistical Papers, Springer, vol. 58(3), pages 911-928, September.
    8. Bai, Z. D. & Guo, Meihui, 1999. "A paradox in least-squares estimation of linear regression models," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 167-174, April.

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