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Bayesian regression on non-parametric mixed-effect models with shape-restricted Bernstein polynomials

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  • Jianhua Ding
  • Zhongzhan Zhang

Abstract

We develop a Bayesian estimation method to non-parametric mixed-effect models under shape-constrains. The approach uses a hierarchical Bayesian framework and characterizations of shape-constrained Bernstein polynomials (BPs). We employ Markov chain Monte Carlo methods for model fitting, using a truncated normal distribution as the prior for the coefficients of BPs to ensure the desired shape constraints. The small sample properties of the Bayesian shape-constrained estimators across a range of functions are provided via simulation studies. Two real data analysis are given to illustrate the application of the proposed method.

Suggested Citation

  • Jianhua Ding & Zhongzhan Zhang, 2016. "Bayesian regression on non-parametric mixed-effect models with shape-restricted Bernstein polynomials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2524-2537, October.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:14:p:2524-2537
    DOI: 10.1080/02664763.2016.1142940
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    Cited by:

    1. Edwin Fourrier-Nicolai & Michel Lubrano, 2022. "Bayesian inference for non-anonymous Growth Incidence Curves using Bernstein polynomials: an application to academic wage dynamics," Working Papers hal-03880243, HAL.
    2. Fourrier-Nicolaï Edwin & Lubrano Michel, 2024. "Bayesian inference for non-anonymous growth incidence curves using Bernstein polynomials: an application to academic wage dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 28(2), pages 319-336, April.

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