Local orthogonal polynomial expansion for density estimation. Issue 4 (2nd October 2017)

• Record Type: Journal Article
• Authors: Amali Dassanayake, D.P.; Volobouev, Igor; Trindade, A. Alexandre
• Is Part Of: Journal of nonparametric statistics. Volume 29:Issue 4(2017)
• Page Start: 806
• Page End: 830
• Publication Date: 2017-10-02
• Subjects: Boundary bias -- kernel density estimation -- local likelihood density estimation -- mean integrated squared error -- orthogonal series density estimation -- sharply truncated support; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2017.1371715
• Languages: English
• ISSNs: 1048-5252

Abstract

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.