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Semi-parametric additive constrained regression

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  • Mary C. Meyer

Abstract

The additive isotonic least-squares regression model has been fit using a sequential pooled adjacent violators algorithm, estimating each isotonic component in turn, and looping until convergence. However, the individual components are not, in general, estimable. The sum of the components, i.e. the expected value of the response, has a unique estimate, which can be found using a single cone projection. Estimators for the individual components are then easily obtained, which are unique if the conditions for estimability hold. Parametrically modelled covariates are easily included in the cone projection specification. The cone structure also provides information about the degrees of freedom of the fit, which can be used in inference methods, variable selection, and estimation of the model variance. Simulations show that these methods can compare favourably to standard parametric methods, even when the parametric assumptions are correct. The estimation and inference methods can be extended to other constraints such as convex regression or isotonic regression on partial orderings.

Suggested Citation

  • Mary C. Meyer, 2013. "Semi-parametric additive constrained regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(3), pages 715-730, September.
  • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:3:p:715-730
    DOI: 10.1080/10485252.2013.797577
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    Cited by:

    1. Sanjida Tasnim, 2021. "Use of Shape Restricted Regression Methods for Fitting Model of Per Capita GDP: A Global Economic Scenario of 2018," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(4), pages 1-52, July.
    2. Yining Chen & Richard J. Samworth, 2016. "Generalized additive and index models with shape constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 729-754, September.
    3. España, Victor J. & Aparicio, Juan & Barber, Xavier & Esteve, Miriam, 2024. "Estimating production functions through additive models based on regression splines," European Journal of Operational Research, Elsevier, vol. 312(2), pages 684-699.
    4. David Conde & Miguel A. Fernández & Cristina Rueda & Bonifacio Salvador, 2021. "Isotonic boosting classification rules," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 289-313, June.
    5. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.

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