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Approximate Confidence Regions

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Book cover Optimal Experimental Design for Non-Linear Models

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

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Abstract

The problem of the approximate confidence regions is discussed, under the light of the introduced measures of nonlinearity. The first order autoregressive model and Michaelis–Menten are discussed as particular cases.

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References

  • Seber CAF, Wild CJ (1989) Nonlinear regression. Wiley, NJ

    Google Scholar 

  • Beale EML (1960) Confidence regions in non-linear estimation. J. Roy. Stat. Soc. B 22:41–88

    MATH  MathSciNet  Google Scholar 

  • Bates DM, Watts DG (1980) Relative curvature measures of nonlinearity. J. Roy. Stat. Soc. B 42:1–25

    MATH  MathSciNet  Google Scholar 

  • Hamilton DC, Watts DC (1985) A quadratic design criterion for precise estimation in nonlinear regression models. Technometrics 27:241–250

    Article  MATH  MathSciNet  Google Scholar 

  • Kitsos CP, Toulias TL (2012) Confidence and tolerance regions for the signal process. Recent Patents on Signal Processing, vol 2

    Google Scholar 

  • Ford I, Titterington DM, Wu CFJ (1985) Inference and sequential design. Biometrika 72:545–551

    Article  MathSciNet  Google Scholar 

  • Michaelis L, Menten ML (1913) Kinetics for intertase action. Biochemische Zeiturg 49:333–369

    Google Scholar 

  • Biebler KE, Schreiber K, Bode R (2008) Solutions to the Michaelis-Menten kinetics are not necessarily unique. In: International conference on computational methods in sciences and engineering (ICCMSE), 2008

    Google Scholar 

  • Endrenyi L, Chan FY (1981) Optimal design of experiments for the estimation of precise hyperbolic kinetic and binding parameters. J Theor Biol 90:241–263

    Article  MathSciNet  Google Scholar 

  • Kitsos CP (2001) Design aspects for the Michaelis–Menten Model. Biometrical Letters 38:53–66

    Google Scholar 

  • Matthews JNS, Allcock GC (2004) Optimal designs for Michaelis-Menten kinetic studies. Stat Med 23:477–491

    Article  Google Scholar 

  • Lai TL, Robbins H (1979) Consistency and asymptotic efficiency of slope estimates in stochastic approximation schemes. Z. Wanhrscheinlichkeitstheorie wer. Gebite 56:329-360

    Google Scholar 

  • Lopez-Fidalgo J, Wong WK (2002) Design issues for the Michaelis-Menten model. J Theor Biol 215:1–11

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Informatics, Technological Educational Institute of Athens, Athens, Greece

    Christos P. Kitsos

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  1. Christos P. Kitsos
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Correspondence to Christos P. Kitsos .

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Kitsos, C.P. (2013). Approximate Confidence Regions. In: Optimal Experimental Design for Non-Linear Models. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45287-1_6

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