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An existence criterion for the nonlinear $$\ell _p$$ ℓ p -norm fitting problem

Author

Listed:
  • Dragan Jukić

    (J.J. Strossmayer University of Osijek)

  • Kristian Sabo

    (J.J. Strossmayer University of Osijek)

Abstract

In this paper, we give a necessary and sufficient criterion for the existence of the $$\ell _p$$ ℓ p -norm estimate for the nonlinear $$\ell _p$$ ℓ p -norm fitting problem. Our criterion is based on the existence level that describes the behavior of the objective function as its argument approaches the extended boundary of the parameter space.

Suggested Citation

  • Dragan Jukić & Kristian Sabo, 2021. "An existence criterion for the nonlinear $$\ell _p$$ ℓ p -norm fitting problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 957-966, September.
    • Handle: RePEc:spr:cejnor:v:29:y:2021:i:3:d:10.1007_s10100-021-00736-7
    DOI: 10.1007/s10100-021-00736-7
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    References listed on IDEAS

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    1. Eugene Demidenko, 2017. "Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 636-665, September.
    2. E. Demidenko, 2008. "Criteria for Unconstrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 375-395, March.
    3. Demidenko, Eugene, 2006. "Criteria for global minimum of sum of squares in nonlinear regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1739-1753, December.
    4. Tadashi Nakamura & Chae-Shin Lee, 1993. "On the existence of minimum contrast estimates in binary response model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 741-758, December.
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