scholarly journals Asymptotics of least-squares estimators for constrained nonlinear regression

1996 ◽  
Vol 24 (3) ◽  
pp. 1316-1326 ◽  
Author(s):  
Jinde Wang
Keyword(s):  
Least Squares ◽  
Nonlinear Regression ◽  
Least Squares Estimators

Consistency Via Type 2 Inequalities: A Generalization of Wu's Theorem

1989 ◽  
Vol 5 (2) ◽  
pp. 272-286 ◽  
Author(s):  
Asad Zaman
Keyword(s):  
Least Squares ◽  
Nonlinear Regression ◽  
New Technique ◽  
Least Squares Estimators ◽  
A New Technique

Wu introduced a new technique for proving consistency of least-squares estimators in nonlinear regression. This paper extends his results in three directions. First, we consider the minimization of arbitrary functions (M-estimators instead of least squares). Second, we use an improved type 2 inequality. Third, an extension of Kronecker's lemma yields a more powerful result.

scholarly journals Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models

Metrika ◽  
2021 ◽  
Author(s):  
Fritjof Freise ◽  
Norbert Gaffke ◽  
Rainer Schwabe
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Parameter Space ◽  
Generalized Linear Models ◽  
Nonlinear Regression ◽  
Linear Models ◽  
Nonlinear Models ◽  
Random Errors ◽  
True Parameter ◽  
Least Squares Estimators

AbstractThe 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 estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

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