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Strong consistency of non-linear least squares estimators in the presence of stochastic regressors

Starke Konsistenz nichtlinearer Kleinste-Quadrate-Schätzer bei stochastischen Regressoren

Consistence forte des estimateurs des moindres carrés non linéaires en présence de variables explicatives aléatoires

Сильная непротиворечивость оценщиков нелинейных наименьщих квадратов при стохастических регрессорах

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Zusammenfassung

Es wird das allgemeine nichtlineare Regressionsmodell mit stochastischen Regressoren und additivem Störterm betrachtet. Es wird gezeigt, daß unter schwachen Voraussetzungen die Folge der Kleinste-Quadrate-Schätzer stark konsistent ist. Die Arbeit verallgemeinert Ergebnisse von Jennrich und Malinvaud.

Summary

A general non linear regression model with stochastic regressors and additive disturbance term is considered. It is shown, that under weak conditions the sequence of least squares estimators is strongly consistent. The paper extends results obtained by Jennrich and Malinvaud.

Résumé

Il est consideré le modèle general non linéaire de régression aux variables explicatives aléatoires et aux résidues additives. Il est démontré que la suite des estimateurs des moindres carrés est fortement consistente sous des conditions faibles. Le present papier généralise des résultats développé par Jennrich et Malinvaud.

Резюме

В этой статье рассматривается общая нелинейная регрессивная модель со стохасткческими регрессорами и аддитивным возмущаюшим термом. Показывается, что при слабых предположениях последовательность оценщиков наименьших квадратов является сильно непротиворечивой. Эта работа обобщает рэзультаты Еннриха и Малинвода.

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Authors
  1. Friedrich Schmid
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Schmid, F. Strong consistency of non-linear least squares estimators in the presence of stochastic regressors. Statistische Hefte 19, 218–230 (1978). https://doi.org/10.1007/BF02932721

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  • DOI: https://doi.org/10.1007/BF02932721

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