Confidence regions in singular weakly nonlinear regression models with constraints

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Lubomír Kubáček
Keyword(s):  
Regression Model ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Confidence Region ◽  
Confidence Regions ◽  
Nonlinear Regression Model ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Linearized Model ◽  
Confidence Ellipsoid

AbstractIt is rather complicated to construct the confidence region in nonlinear regression model mainly when number of parameters is large. If the nonlinearity of the model is weak, then it is possible, after some modification, to approximate the confidence region by a confidence ellipsoid in the linearized model. The aim of the paper is to propose a solution in singular models with constraints.

Early LOC Estimation of Web Apps Created Using Yii Framework by Nonlinear Regression Models

2021 ◽  
Vol 20 ◽  
pp. 321-328
Author(s):  
Sergiy Prykhodko ◽  
Ivan Shutko ◽  
Andrii Prykhodko
Keyword(s):  
Regression Model ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Web Applications ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models ◽  
Normalizing Transformations ◽  
Box Cox Transformation ◽  
Decimal Logarithm

We have performed early LOC estimation of Web applications (apps) created using the Yii framework by three nonlinear regression models with three predictors based on the normalizing transformations. We used two univariate transformations (the decimal logarithm and the Box-Cox transformation) and the Box-Cox four-variate transformation for constructing nonlinear regression models. The nonlinear regression model constructed by the Box-Cox four-variate transformation has better size prediction results compared to other regression ones based on the univariate transformations.

Reparameterization of weakly nonlinear regression models with constraints

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Lubomír Kubáček ◽  
Gejza Wimmer
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Confidence Regions ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Parameter Estimators

AbstractThere are several ways how to redefine the Bates and Watts curvatures in models with constraints. One of possible approaches is based on a reparametrization of models. It enables us to construct linearization regions for the bias of parameter estimators, for the confidence regions, etc., in an easy way.

scholarly journals A Memoir on Nonlinear Regression Model and its Pseudo Model

2018 ◽  
Vol 7 (4.10) ◽  
pp. 995
Author(s):  
B. Mahaboob ◽  
J. PeterPraveen ◽  
J. Ravi Sankar ◽  
B. Venkateswarlu ◽  
C. Narayana
Keyword(s):  
Regression Model ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Applied Mathematics ◽  
Second Order ◽  
Nonlinear Regression Model ◽  
Linear Regression Models ◽  
Estimation Of Parameters ◽  
Nonlinear Regression Models ◽  
Pseudo Second Order

The main objective of this article is to specify a nonlinear regression model, formulate the assumptions on them and aquire its linear pseudo model. A model may be considered a mathematical description of a physical, chemical or biological state or process. Many models used in applied mathematics and Mathematical statistics are nonlinear in nature one of the major topics in the literature of theoretical and applied mathematics is the estimation of parameters of nonlinear regression models. A perfect model may have to many parameters to be useful. Nonlinear regression models have been intensively studied in the last three decades. Junxiong Lin et.al [1] , in their paper, compared best –fit equations of linear and nonlinear  forms of two widely used kinetic models, namely pseudo-first order and pseudo=second-order equations. K. Vasanth kumar [2], in his paper, proposed five distinct models of second order pseudo expression and examined a comparative study between method of least squares for linear regression models and a trial and error nonlinear regression procedures of deriving pseudo second order rare kinetic parameters. Michael G.B. Blum et.al [3] proposed a new method which fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics and then adaptively improves estimation using importance sampling.  

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models

2015 ◽  
Vol 65 (2) ◽  
Author(s):  
Lubomír Kubáček
Keyword(s):  
Nonlinear Regression ◽  
Statistical Models ◽  
Regression Models ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Statistical Hypotheses ◽  
Linear Statistical Models

AbstractWeakly nonlinear hypothesis on parameters in nonlinear regression models can be tested by methods of linear statistical models in some cases. Certain conditions must be satisfied. The aim of the paper is to find them for models without/with constraints on parameters.

scholarly journals Application of Statistical Methods to the Assessment of Prices of Klaipeda City Apartments

2014 ◽  
Vol 53 (1) ◽  
pp. 64-77
Author(s):  
Roberta Navickaitė
Keyword(s):  
Real Estate ◽  
Regression Model ◽  
Statistical Methods ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Additive Model ◽  
Nonlinear Regression Model ◽  
Generalised Additive Model ◽  
Parametric Regression ◽  
Real Estate Valuation

The paper analyses the use of a nonlinear regression model, generalised linear model and generalised additive model(semi-parametric regression model) for creating real estate valuation models. These models are applied to data on transactions inKlaipeda city apartments. The aim is to create real estate valuation regression models applying various statistical methods and tocompare them with each other. The practical aspects of creating regression models are analysed and conclusions are presented in thepaper.

scholarly journals Estimating the Efforts of Mobile Application Development in the Planning Phase Using Nonlinear Regression Analysis

2020 ◽  
Vol 25 (2) ◽  
pp. 172-179
Author(s):  
Sergiy Prykhodko ◽  
Natalia Prykhodko ◽  
Kateryna Knyrik
Keyword(s):  
Regression Model ◽  
Nonlinear Regression ◽  
Mobile Application ◽  
Regression Models ◽  
Multiple Regression Model ◽  
Application Development ◽  
Nonlinear Regression Models ◽  
Planning Phase ◽  
Mobile Application Development ◽  
Decimal Logarithm

AbstractThe authors consider the construction of a nonlinear multiple regression model, its confidence and prediction intervals to evaluate the efforts of mobile application development in the planning phase based on the multivariate normalizing transformation and outlier detection. The constructed model is compared to the linear regression model and nonlinear regression models based on the univariate transformations, such as the decimal logarithm, Box–Cox, and Johnson transformation. This model, in comparison with other regression models, has better prediction accuracy.

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