Strong consistency of least squares estimates with i.i.d. errors with mean values not necessarily defined |
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Authors: | João Lita da Silva João Tiago Mexia |
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Institution: | 1. Department of Mathematics, Faculty of Sciences and Technology , New University of Lisbon , Quinta da Torre, 2829-516 Caparica, Lisbon , Portugal jfls@fct.unl.pt;3. Department of Mathematics, Faculty of Sciences and Technology , New University of Lisbon , Quinta da Torre, 2829-516 Caparica, Lisbon , Portugal |
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Abstract: | We establish strong consistency of the least squares estimates in multiple regression models discarding the usual assumption of the errors having null mean value. Thus, we required them to be i.i.d. with absolute moment of order r, 0<r<2, and null mean value when r>1. Only moderately restrictive conditions are imposed on the model matrix. In our treatment, we use an extension of the Marcinkiewicz–Zygmund strong law to overcome the errors mean value not being defined. In this way, we get a unified treatment for the case of i.i.d. errors extending the results of some previous papers. |
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Keywords: | least squares estimates regression models strong consistency Marcinkiewicz–Zygmund law undefined errors mean values |
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