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A least squares-type density estimator using a polynomial function

Author

Listed:
  • Im, Jongho
  • Morikawa, Kosuke
  • Ha, Hyung-Tae

Abstract

Higher-order density approximation and estimation methods using orthogonal series expansion have been extensively discussed in statistical literature and its various fields of application. This study proposes least squares-type estimation for series expansion via minimizing the weighted square difference of series distribution expansion and a benchmarking distribution estimator. As the least squares-type estimator has an explicit expression, similar to the classical moment-matching technique, its asymptotic properties are easily obtained under certain regularity conditions. In addition, we resolve the non-negativity issue of the series expansion using quadratic programming. Numerical examples with various simulated and real datasets demonstrate the superiority of the proposed estimator.

Suggested Citation

  • Im, Jongho & Morikawa, Kosuke & Ha, Hyung-Tae, 2020. "A least squares-type density estimator using a polynomial function," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302373
    DOI: 10.1016/j.csda.2019.106882
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    References listed on IDEAS

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    1. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-1525, September.
    2. Lan Xue & Jing Wang, 2010. "Distribution function estimation by constrained polynomial spline regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 443-457.
    3. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    4. Efromovich, Sam, 1996. "Adaptive orthogonal series density estimation for small samples," Computational Statistics & Data Analysis, Elsevier, vol. 22(6), pages 599-617, October.
    5. Hall, Peter, 1982. "Comparison of two orthogonal series methods of estimating a density and its derivatives on an interval," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 432-449, September.
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