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Shape testing in varying coefficient models

Author

Listed:
  • M. Ahkim

    (Universiteit Antwerpen)

  • I. Gijbels

    (KU Leuven)

  • A. Verhasselt

    (Universiteit Hasselt)

Abstract

We consider varying coefficient models which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (often time). Varying coefficient models have been popular in longitudinal data and panel data studies, and have been applied in fields, such as finance and health sciences. We estimate the coefficient functions by splines. An important question in a varying coefficient model is whether a coefficient function is monotone or convex. We develop consistent testing procedures for monotonicity and convexity. Moreover, we provide procedures to test simultaneously the shapes of certain coefficient functions in a varying coefficient model. The tests use constrained and unconstrained regression splines. The performances of the proposed tests are illustrated on simulated data. We also give a real data application.

Suggested Citation

  • M. Ahkim & I. Gijbels & A. Verhasselt, 2017. "Shape testing in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 429-450, June.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0518-y
    DOI: 10.1007/s11749-016-0518-y
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    References listed on IDEAS

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    1. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
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    Cited by:

    1. Tatiana Komarova & Javier Hidalgo, 2019. "Testing nonparametric shape restrictions," Papers 1909.01675, arXiv.org, revised Jun 2020.
    2. Gao, Zhikun & Tang, Yanlin & Wang, Huixia Judy & Wu, Guangying K. & Lin, Jeff, 2020. "Automatic identification of curve shapes with applications to ultrasonic vocalization," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    3. Ghosal, Rahul & Ghosh, Sujit & Urbanek, Jacek & Schrack, Jennifer A. & Zipunnikov, Vadim, 2023. "Shape-constrained estimation in functional regression with Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).

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