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A New Class of Consistent Estimators for Stochastic Linear Regressive Models


  • An, Hong-Zhi
  • Hickernell, Fred J.
  • Zhu, Li-Xing


In this paper we propose a new approach for estimating the unknown parameter in the stochastic linear regressive model with stationary ergodic sequence of covariates. Under mild conditions on the joint distribution of the covariate and the error, the estimator constructed is shown to be strongly consistent in two important special cases: (1) The sequence of (variate, covariate) is independent identically distributed (i.i.d.), and (2) the sequence of variates is a stationary autoregressive series. The asymptotical normality is also discussed under more assumptions on the distribution of the covariate.

Suggested Citation

  • An, Hong-Zhi & Hickernell, Fred J. & Zhu, Li-Xing, 1997. "A New Class of Consistent Estimators for Stochastic Linear Regressive Models," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 242-258, November.
  • Handle: RePEc:eee:jmvana:v:63:y:1997:i:2:p:242-258

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    References listed on IDEAS

    1. Abdous, B. & Theodorescu, R., 1992. "Note on the spatial quantile of a random vector," Statistics & Probability Letters, Elsevier, vol. 13(4), pages 333-336, March.
    2. Masse, J. C. & Theodorescu, R., 1994. "Halfplane Trimming for Bivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 48(2), pages 188-202, February.
    3. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    4. Eaton, Morris L. & Perlman, Michael D., 1991. "Concentration inequalities for multivariate distributions: I. multivariate normal distributions," Statistics & Probability Letters, Elsevier, vol. 12(6), pages 487-504, December.
    5. Nolan, D., 1992. "Asymptotics for multivariate trimming," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 157-169, August.
    6. Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
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