Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지

Statistical Estimation and Algorithm in Nonlinear Functions

  • Jea-Young Lee (Department of Statistics, Yeungnam Unicersity, Gyongsan, 712-749, KOREA)
  • Published : 1995.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

A new algorithm was given to successively fit the multiexponential function/nonlinear function to data by a weighted least squares method, using Gauss-Newton, Marquardt, gradient and DUD methods for convergence. This study also considers the problem of linear-nonlimear weighted least squares estimation which is based upon the usual Taylor's formula process.

Keywords

References

  1. Nonlinear Parameter Estimation Bard,Jonathan
  2. The American Statistics v.46 no.4 Deriving generalized means as least squares and maximum likelihood estimates Berger,R.L.;Cassella,George
  3. Journal of Royal Statistical Society v.B32 Bias in nonlinear estimation Box,M.J.
  4. Linear Models for Multivariate, Time-series, and Spatial Data Christensen,R.
  5. Plane answers to Complex Questions Christensen,R.
  6. Biomatrika v.72 no.1 Residuals in nonlinear regression Cook,R.D.;Tsai,C.
  7. Circulation Research v.32 A weighted least-squares technique for the analysis of kinetic data and its application to the study of renal xenon washout in dogs and man Dell,R.B.;Sciacca,R.;Lieberman,K.;Case,D.B.;Cannon,P.J.
  8. Americal Journal of Physiology v.246 Multiexponential, multicompartmental, and noncompartmental modeling. I. Methodological limitations and physioligical interpretations DiStefano III,J.J.;Landaw,E.M.
  9. American Statistician v.29 no.2 Nonlinear Regression Gallant,A.R.
  10. Technometrics v.3 Modified Gauss-Newton method for the fitting of nonlinear regression functions by least squares Hartley,H.O.
  11. Americal Journal of Physiology v.246 Multiexponential, multicompartmental, and noncompartmental modeling. II. Data analysis ans statistical considerations Landaw,E.M.;DiStefano III,J.J.
  12. Testing Statistical Hypothesis(2nd ed.) Lehmann,E.L.
  13. Journal of the Society for Industrial and Applied Mathematics v.11 An algorithm for least squares estimation of nonlinear parameters Marquardt,D.W.
  14. Technometrics v.1 DUD, a derivative-free algorithm for nonlinear least squares Ralston,M.L.;Jennrich,R.L.
  15. Annals of Mathematical Statistics v.40 no.2 On the least squares estimation of nonlinear relations Villegas,C.