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A Projection Approach to Monotonic Regression with Bernstein Polynomials

ZHU Guo, FANG Xiangzhong   

  1. School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2020-12-15 Revised:2021-07-24 Online:2022-10-25 Published:2022-10-12
  • Supported by:
    This research was supported by Science Challenge Project under Grant No.TZ2018001.

ZHU Guo, FANG Xiangzhong. A Projection Approach to Monotonic Regression with Bernstein Polynomials[J]. Journal of Systems Science and Complexity, 2022, 35(5): 1910-1928.

Monotonic regression problems have been widely seen in many fields like economics and biostatistics.Usually the monotonic parameter space is used by the Bayesian methods using Bernstein polynomials.In this paper the authors extend the usual parameter space to a larger space in which all the proper parameters making the regression function to be monotonic are included.In order to ensure that the problem could be solved in the new parameter space,the authors use a projection posterior method to make inference.The authors show the proposed method has good approximation properties and performs well compared with other competing methods both in simulations and in practical applications.
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