Bias reduction by transformed flat-top Fourier series estimator of density on compact support. Issue 4 (2nd October 2022)

• Record Type: Journal Article
• Authors: Wang, Liang; Politis, Dimitris N.
• Is Part Of: Journal of nonparametric statistics. Volume 34:Issue 4(2022)
• Page Start: 831
• Page End: 858
• Publication Date: 2022-10-02
• Subjects: Nonparametric density estimation -- Gibbs phenomenon -- higher order of bias -- hypothesis testing; 62G07 -- 62F03; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2022.2078821
• Languages: English
• ISSNs: 1048-5252

Abstract

Abstract : The problem of nonparametric estimation of a univariate density with r th continuous derivative on compact support is addressed ( r ≥ 2 ). If the density function has compact support and is non-zero at either boundary, regular kernel estimator will be completely biased at such boundary. Although several correction methods were proposed to improve the bias at the boundary to h 2 in the last decades, this paper initiates a way to further improve bias to higher order ( h r ) for interior area of density function support, while remaining the order of bias h 2 at boundary. We will first review flat-top kernel estimator and flat-top series estimator, then propose the Transformed Flat-top Series estimator. The theoretical analysis is supplemented with simulation results as well as real data applications.