Consistent Directions of the Least Squares Estimators in Linear Models.

1982 ◽  
Author(s):  
Song-Gui Wang ◽  
C. F. Jeff Wu
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Least Squares Estimators

scholarly journals Sensitivity analysis in linear models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Shuangzhe Liu ◽  
Tiefeng Ma ◽  
Yonghui Liu
Keyword(s):  
Sensitivity Analysis ◽  
Least Squares ◽  
Linear Model ◽  
Linear Models ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
The Other ◽  
Regression Coefficients ◽  
General Linear ◽  
Least Squares Estimators

AbstractIn this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

On the Asymptotic Distribution of the Least-Squares Estimators in Unidentifiable Models

2004 ◽  
Vol 16 (1) ◽  
pp. 99-114 ◽  
Author(s):  
Taichi Hayasaka ◽  
Masashi Kitahara ◽  
Shiro Usui
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Linear Models ◽  
Stochastic Property ◽  
Learning Machines ◽  
Least Squares Estimators

In order to analyze the stochastic property of multilayered perceptrons or other learning machines, we deal with simpler models and derive the asymptotic distribution of the least-squares estimators of their parameters. In the case where a model is unidentified, we show different results from traditional linear models: the well-known property of asymptotic normality never holds for the estimates of redundant parameters.

When BLUE is not best: non-normal errors and the linear model

2018 ◽  
Vol 8 (1) ◽  
pp. 136-148 ◽  
Author(s):  
Daniel K. Baissa ◽  
Carlisle Rainey
Keyword(s):  
Monte Carlo ◽  
Statistical Theory ◽  
Monte Carlo Simulations ◽  
Least Squares ◽  
Political Science ◽  
Linear Model ◽  
Linear Models ◽  
Least Squares Estimators ◽  
Data Points ◽  
Least Squares Estimates

AbstractResearchers in political science often estimate linear models of continuous outcomes using least squares. While it is well known that least-squares estimates are sensitive to single, unusual data points, this knowledge has not led to careful practices when using least-squares estimators. Using statistical theory and Monte Carlo simulations, we highlight the importance of using more robust estimators along with variable transformations. We also discuss several approaches to detect, summarize, and communicate the influence of particular data points.

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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