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Strong consistency of least squares estimates in multiple regression models with random regressors

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  • João Lita da Silva

Abstract

The strong consistency of the least squares estimator in multiple regression models is established assuming the randomness of the regressors and errors with infinite variance. Only moderately restrictive conditions are imposed on the stochastic model matrix and the errors will be random variables having moment of order $$r,\,1 \leqslant r \leqslant 2$$ . In our treatment, we use Etemadi’s strong law of large numbers and a sharp almost sure convergence for randomly weighted sums of random elements. Both techniques permit us to extend the results of some previous papers. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • João Lita da Silva, 2014. "Strong consistency of least squares estimates in multiple regression models with random regressors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 361-375, April.
    • Handle: RePEc:spr:metrik:v:77:y:2014:i:3:p:361-375
    DOI: 10.1007/s00184-013-0443-y
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    References listed on IDEAS

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    1. Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
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