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Weak consistency of least-squares estimators in linear models

Author

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  • Kaffes, D.
  • Bhaskara Rao, M.

Abstract

Let Yn, n>=1, be a sequence of integrable random variables with EYn = xn1[beta]1 + xn2[beta]2 + ... + xnp[beta]p, where the xij's are known and [beta]T = ([beta]1, [beta]2,..., [beta]p) unknown. Let bn be the least-squares estimator of [beta] based on Y1, Y2,..., Yn. Weak consistency of bn, n>=1, has been considered in the literature under the assumption that each Yn is square integrable. In this paper, we study weak consistency of bn, n>=1, and associated rates of convergence under the minimal assumption that each Yn is integrable.

Suggested Citation

  • Kaffes, D. & Bhaskara Rao, M., 1982. "Weak consistency of least-squares estimators in linear models," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 186-198, June.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:2:p:186-198
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    Cited by:

    1. Chen, Pingyan & Hao, Chunyan, 2011. "A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1808-1812.
    2. Ko, Mi-Hwa, 2013. "On complete convergence for weighted sums of asymptotically linear negatively dependent random field," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2615-2620.

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