In this article, the asymptotic normality and strong consistency of the least square estimators for the unknown parameters in the simple linear errors in variables model are established under the assumptions that the errors are stationary negatively associated sequences. Copyright...

The paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares...

This paper presents a new random weighting method to estimation of the stable exponent. Assume that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X_1, X_2, \ldots ,X_n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>X</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>X</mi> <mi>n</mi> </msub> </mrow> </math> </EquationSource> </InlineEquation> is a sequence of independent and identically distributed random variables with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi mathvariant="italic">α</mi> </math> </EquationSource> </InlineEquation>-stable distribution G, where <InlineEquation ID="IEq3"> <EquationSource...</equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

A vector autoregression with deterministic terms and with no restrictions to its characteristic roots is considered. Strong consistency results and also some weak convergence results are given for a number of least squares statistics. These statistics are related to the denominator matrix of the...