Least Squares Method of Estimation Using Bernstein Polynomials for Density Estimation

Authors

  • Piyada Thongjaem Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, PathumThani 12120, Thailand.
  • Sujit K. Ghosh Department of Statistics, NC State University, Raleigh, NC USA.
  • Kamon Budsaba Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, PathumThani 12120, Thailand.

Keywords:

Bernstein polynomials, density estimation, nonparametric method, constraints least squares method

Abstract

A novel method is used to convert the density estimation to the well-known problem of weighted least squares subject to restrictions on parameters. In turn, the problem is solved using the efficient quadratic programming method. Numerous simulation studies are performed to fast the validity of the proposed method and it is shown that mean integrated squared errors (MISE) of density estimator is smaller than standard estimator. There are various values of MISE at different degree of Bernstein polynomials, m. From our method, the MISE at m optimal will have the lowest value compared with other m. This result proved that m optimal is suitable to achieve the best density estimation. At the m optimal, comparing with Kernel method, the Bernstein polynomials can provide better (less) MISE for all simulated types of probability function.

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How to Cite

Thongjaem, P., Ghosh, S. K., & Budsaba, K. (2015). Least Squares Method of Estimation Using Bernstein Polynomials for Density Estimation. Thailand Statistician, 11(1), 45–65. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34216

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