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The stochastic restricted ridge estimator in generalized linear models

Author

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  • M. Revan Özkale

    (Çukurova University)

  • Hans Nyquist

    (Stockholm University)

Abstract

Many researchers have studied restricted estimation in the context of exact and stochastic restrictions in linear regression. Some ideas in linear regression, where the ridge and restricted estimations are the well known, were carried to the generalized linear models which provide a wide range of models, including logistic regression, Poisson regression, etc. This study considers the estimation of generalized linear models under stochastic restrictions on the parameters. Furthermore, the sampling distribution of the estimators under the stochastic restriction, the compatibility test and choice of the biasing parameter are given. A real data set is analyzed and simulation studies concerning Binomial and Poisson distributions are conducted. The results show that when stochastic restrictions and ridge idea are simultaneously applied to the estimation methods, the new estimator gains efficiency in terms of having smaller variance and mean square error.

Suggested Citation

  • M. Revan Özkale & Hans Nyquist, 2021. "The stochastic restricted ridge estimator in generalized linear models," Statistical Papers, Springer, vol. 62(3), pages 1421-1460, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01142-7
    DOI: 10.1007/s00362-019-01142-7
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    References listed on IDEAS

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    1. Groß, Jürgen, 2003. "Restricted ridge estimation," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 57-64, October.
    2. Özkale, M. Revan, 2009. "A stochastic restricted ridge regression estimator," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1706-1716, September.
    3. R. Fallah & M. Arashi & S. M. M. Tabatabaey, 2017. "On the ridge regression estimator with sub-space restriction," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(23), pages 11854-11865, December.
    4. Hans Nyquist, 1991. "Restricted Estimation of Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 133-141, March.
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    Cited by:

    1. M. Revan Özkale & Atif Abbasi, 2022. "Iterative restricted OK estimator in generalized linear models and the selection of tuning parameters via MSE and genetic algorithm," Statistical Papers, Springer, vol. 63(6), pages 1979-2040, December.

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