A Monograph on Nonlinear Regression Models

  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract

    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.



  • Keywords

    Nonlinear regression model, Residual form of Squares, error variance, Least Squares Estimator, Parametric vector, variance-Covariance matrix, OLS.

  • References

      [1] Arthipova Irina, Arthipovs Sergejs, “Application of Ordinary Least Square Method in Nonlinear models”, International statistical Institute, 56th session, (2007).

      [2] MA Tabatabai, JJ Kengwoung Keuomo and K. P. Singh, “A new Robust method for nonlinear regression”, Journal of biometrics and biostatistics, Vol. (5). (2014).

      [3] Xu Zheng, “Testing heteroscedasticity in nonlinear and nonparametric regression”, Canadian Journal of statistics, Vol. (37), issue 2, (2009), Pp: 282-300.

      [4] Gordon K. Smyth, “Nonlinear regression, Encyclopedia of Environ metrics Vol. (3), (2002), Pp: 1405-1411

      [5] Gurleen K. Popli , “A note on the instrumental variable estimators in the nonlinear models”, Journal of Quantitative Economics Vol.16. no.2, (2000), Pp: 31-36.

      [6] Davidian M. and Giltinon D.M, “Nonlinear models for repeated measurement Data: An overview and update”, Journal of Agricultural, Biological and Environmental statistics (JABES), Vol. (8), (2003), Pp: 387-419.

      [7] Vasilyev D.M, “Theoretical and Practical Aspects of linear and nonlinear models order reduction Techniques”, MIT, USA, (2008).

      [8] E. Grafarent and J. Awange, “Application of linear and nonlinear models”, Springer Geophysics, (2012).

      [9] Bates D.M and Walts D.G, “Nonlinear regression: Iterative Estimation and Linear Approximations in Nonlinear regression Analysis and its Applications”, John Wiley and sons Inc Hobeken, NJ, USA, (2008).




Article ID: 21277
DOI: 10.14419/ijet.v7i4.10.21277

Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.