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Efficient discriminating design for a class of nested polynomial regression models

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Abstract

This paper studies efficient designs for simultaneous model discrimination among polynomial regression models up to degree k. Based on the \({\Phi_{\boldsymbol{\beta}}}\) -optimality criterion proposed by Dette (Ann Stat 22:890–903, 1994), a maximin \({\Phi_{\boldsymbol{\beta}^{*}}}\) -optimal discriminating design is derived in terms of canonical moments for \({k\in\mathbb{N}}\) . Theoretical and numerical results show that the proposed design performs well for model discrimination in most of the considered models.

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References

  • Atkinson AC (1972) Planning experiments to detect inadequate regression models. Biometrika 59: 275–293

    Article  MathSciNet  MATH  Google Scholar 

  • Atkinson AC, Cox DR (1974) Planning experiments for discriminating between models (with discussion). J R Stat Soc Ser B 36: 321–348

    MathSciNet  MATH  Google Scholar 

  • Atkinson AC, Fedorov VV (1975a) The design of experiments for discriminating between two rival models. Biometrika 62: 57–70

    Article  MathSciNet  MATH  Google Scholar 

  • Atkinson AC, Fedorov VV (1975b) Optimal design: experiments for discriminating between several models. Biometrika 62: 289–303

    MathSciNet  MATH  Google Scholar 

  • Biedermann S, Dette H, Hoffmann P (2009) Constrained optimal discrimination designs for Fourier regression models. Ann Inst Stat Math 61: 143–157

    Article  MathSciNet  MATH  Google Scholar 

  • Dette H (1994) Discrimination designs for polynomial regression on compact intervals. Ann Stat 22: 890–903

    Article  MathSciNet  MATH  Google Scholar 

  • Dette H (1995) Optimal designs for identifying the degree of a polynomial regression. Ann Stat 23: 1248–1266

    Article  MathSciNet  MATH  Google Scholar 

  • Dette H, Franke T (2000) Constrained D- and D 1-optimal designs for polynomial regression. Ann Stat 28: 1702–1727

    Article  MathSciNet  MATH  Google Scholar 

  • Dette H, Franke T (2001) Robust designs for polynomial regression by maximizing a minimum of D- and D 1-efficiencies. Ann Stat 29: 1024–1049

    Article  MathSciNet  MATH  Google Scholar 

  • Dette H, Haller G (1998) Optimal designs for the identification of the order of a Fourier regression. Ann Stat 26: 1496–1521

    Article  MathSciNet  MATH  Google Scholar 

  • Dette H, Röder I (1997) Optimal discrimination designs for multifactor experiments. Ann Stat 25: 1161–1175

    Article  MATH  Google Scholar 

  • Dette H, Studden WJ (1997) The theory of canonical moments with applications in statistics, probability, and analysis. Wiley, New York

    MATH  Google Scholar 

  • Kiefer JC, Wolfowitz J (1959) Optimum designs in regression problems. Ann Math Stat 30: 271–294

    Article  MathSciNet  MATH  Google Scholar 

  • Lau TS (1983) Theory of canonical moments and its application in polynomial regression, I and II. Technical Reports 83-23 and 83-24, Department of Statistics, Purdue University

  • Lau TS (1988) D-optimal designs on the unit q-ball. J Stat Plan Inference 19: 299–315

    Article  MATH  Google Scholar 

  • Läuter E (1974) Experimental design in a class of models. Math Oper Stat 5: 379–398

    Google Scholar 

  • Skibinsky M (1967) The range of the (n + 1)th moment for distributions on [0,1]. J Appl Probab 4: 543–552

    Article  MathSciNet  MATH  Google Scholar 

  • Skibinsky M (1968) Extreme nth moments for distributions on [0,1] and the inverse of a moment space map. J Appl Probab 5: 693–701

    Article  MathSciNet  MATH  Google Scholar 

  • Skibinsky M (1986) Principal representations and canonical moment sequences for distributions on an interval. J Math Anal Appl 120: 95–118

    Article  MathSciNet  MATH  Google Scholar 

  • Stigler SM (1971) Optimal experimental design for polynomial regression. J Am Stat Assoc 66: 311–318

    MATH  Google Scholar 

  • Studden WJ (1982) Some robust-type D-optimal designs in polynomial regression. J Am Stat Assoc 77: 916–921

    MathSciNet  MATH  Google Scholar 

  • Tsai MH (2011) A note on Läuter-type robust design for polynomial regression models. J Stat Plan Inference 141: 1958–1967

    Article  MATH  Google Scholar 

Download references

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  1. Department of Statistics, National Taipei University, New Taipei City, 23741, Taiwan

    Min-Hsiao Tsai

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  1. Min-Hsiao Tsai
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Correspondence to Min-Hsiao Tsai.

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Tsai, MH. Efficient discriminating design for a class of nested polynomial regression models. Metrika 75, 809–817 (2012). https://doi.org/10.1007/s00184-011-0353-9

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  • DOI: https://doi.org/10.1007/s00184-011-0353-9

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