On the consistency of \(l_ \alpha\)-estimators of parameters of a regression function. (English. Russian original) Zbl 0748.62035

Ivanov, A. V.

Theory Probab. Math. Stat. 42, 47-53 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 42-48 (1990).

Summary: For a nonlinear regression model, conditions for the consistency of estimators of an unknown parameter obtained by minimizing the \(l_ \alpha\)-norm \((1<\alpha < 2)\) of the residuals of observations are derived. The results obtained generalize the analogous assertions about the least squares estimators \((\alpha=2)\) and the least absolute value \((\alpha=1)\) estimators.

MSC:

62J02	General nonlinear regression
62F12	Asymptotic properties of parametric estimators
62E20	Asymptotic distribution theory in statistics

Keywords:

least absolute value estimators; consistency of estimators; residuals of observations; least squares estimators; l(alpha)-norms