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Reparameterization of weakly nonlinear regression models with constraints

  • Lubomír Kubáček EMAIL logo und Gejza Wimmer
Veröffentlicht/Copyright: 27. August 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 3

Abstract

There 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.

Key words: nonlinear regression model; reparametrization; Bates and Watts curvatures; linearization
MSC 2010: Primary 62F10; 62J05

Supported by the Council of the Czech Government MSM 6 198 959 214

(Communicated by Gejza Wimmer)

Acknowledgement

Autor is indebted to RNDr. J. Marek, Ph.D. for his help in numerical calculation and to the reviewer who recognized many mistakes in the manuscript.

References

[1] Bates, D. M.—Watts, D. G.: Relative curvature measures of nonlinearity, J. Roy. Statist. Soc. Ser. B 42 (1980), 1–25.10.1111/j.2517-6161.1980.tb01094.xSuche in Google Scholar

[2] Fišerová, E.—Kubáček, L.—Kunderová, P.: Linear Statistical Models; Regularity and Singularities, Academia, Prague, 2007.Suche in Google Scholar

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[4] Kubáček, L.—Tesaříková, E.: Weakly nonlinear regression model with constraints I: nonlinear hypothesis, Discuss. Math. Probab. Stat. 25 (2005), 115–133.10.7151/dmps.1065Suche in Google Scholar

[5] Kubáček, L.—Tesaříková, E.: Weakly Nonlinear Regression Models, Palacký University, Olomouc, 2008.Suche in Google Scholar

[6] Rao, C. R.—Mitra, S. K.: Generalized Inverse of Matrices and Its Applications, J. Wiley, New York-London-Sydney-Toronto, 1971.Suche in Google Scholar

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Received: 2012-11-30
Accepted: 2013-11-15
Published Online: 2016-8-27
Published in Print: 2016-6-1

© Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0175
Schlagwörter für diesen Artikel
nonlinear regression model; reparametrization; Bates and Watts curvatures; linearization

Artikel in diesem Heft

  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
  16. A construction of a Peano curve
  17. Research Article
  18. Compositions of ϱ-upper continuous functions
  19. Research Article
  20. Products of Świa̧tkowski functions
  21. Research Article
  22. Subclasses of meromorphically p-valent functions involving a certain linear operator
  23. Research Article
  24. Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments
  25. Research Article
  26. Oscillation criteria for higher order nonlinear delay dynamic equations on time scales
  27. Research Article
  28. On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
  29. Research Article
  30. Meromorphic solutions of q-shift difference equations
  31. Research Article
  32. Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales
  33. Research Article
  34. Multiplier spaces and the summing operator for series
  35. Research Article
  36. Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operators
  37. Research Article
  38. The local spectral radius of a nonnegative orbit of compact linear operators
  39. Research Article
  40. A note on Lie product preserving maps on Mn(ℝ)
  41. Research Article
  42. On vector optimality conditions for constrained problems with ℓ-stable data
  43. Research Article
  44. Reparameterization of weakly nonlinear regression models with constraints
  45. Research Article
  46. Convolutions of polynomial kernels
  47. Research Article
  48. Closed form evaluation of sums containing squares of Fibonomial coefficients
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