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Local orthogonal polynomial expansion for density estimation

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  • D.P. Amali Dassanayake
  • Igor Volobouev
  • A. Alexandre Trindade

Abstract

A local orthogonal polynomial expansion (LOrPE) of the empirical density function is proposed as a novel method to estimate the underlying density. The estimate is constructed by matching localised expectation values of orthogonal polynomials to the values observed in the sample. LOrPE is related to several existing methods, and generalises straightforwardly to multivariate settings. By manner of construction, it is similar to local likelihood density estimation (LLDE). In the limit of small bandwidths, LOrPE functions as kernel density estimation (KDE) with high-order (effective) kernels inherently free of boundary bias, a natural consequence of kernel reshaping to accommodate endpoints. Consistency and faster asymptotic convergence rates follow. In the limit of large bandwidths LOrPE is equivalent to orthogonal series density estimation (OSDE) with Legendre polynomials, thereby inheriting its consistency. We compare the performance of LOrPE to KDE, LLDE, and OSDE, in a number of simulation studies. In terms of mean integrated squared error, the results suggest that with a proper balance of the two tuning parameters, bandwidth and degree, LOrPE generally outperforms these competitors when estimating densities with sharply truncated supports.

Suggested Citation

  • D.P. Amali Dassanayake & Igor Volobouev & A. Alexandre Trindade, 2017. "Local orthogonal polynomial expansion for density estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 806-830, October.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:4:p:806-830
    DOI: 10.1080/10485252.2017.1371715
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    References listed on IDEAS

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