A Memoir on Nonlinear Regression Model and its Pseudo Model

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    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.

     

     


  • Keywords


    Nonlinear regression model, variance covariance matrix, linear pseudo model, least squares estimator, degrees of freedom.

  • References


      [1] Michael G. B. Blum, Olivier Franwis (2010), “Nonlinear regression models for Appropriate Bayesian computation”, Statistics and Computing, Springer, Vol. (20), Issue 1, Pp: 63-73.

      [2] Shyamal D Peddada, Joseph K. Haseman, “Analysis of Nonlinear regression models. A Cautionary note”, Dose-Response: An international journal Vol. (3), Issue 4, (2005).

      [3] K. Vasanth Kumar, “Linear and Nonlinear regression analysis for the sorption kinetics methylene blue onto activated Carbon”, Journal of Hazardous Materials B137, (2006), Pp: 1538-1544.

      [4] Junxiong Lin, Lan Wang, “Comparison between linear and nonlinear forms of Pseudo-first order and pseudo-second order adoption kinetic models for the removal of methylene blue by activated carbon”, Frontiers of Environmental Science and Engineering in China, Vol.(3), Issue 3, (2009), Pp: 320-324.

      [5] Gordon K. Sonyth, “Nonlinear regression, Encyclopaedia of Environ metrics Vol. (3), (2002), Pp: 1405-1461.

      [6] 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.

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

      [8] 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).

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

      [10] 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.


 

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Article ID: 26643
 
DOI: 10.14419/ijet.v7i4.10.26643




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