Adaptive Fourier tester for statistical estimation. (16th March 2016)

• Record Type: Journal Article
• Authors: Chen, Qiuhui; Qian, Tao; Li, Yuan; Mai, Weixiong; Zhang, Xingfa
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 12(2016:Aug. 15)
• Page Start: 3478
• Page End: 3495
• Publication Date: 2016-03-16
• Subjects: TM estimator -- Hardy space -- Cayley transform -- adaptive -- approximation order; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3795
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : Based on Takenaka–Malmquist (TM) system, a new nonparametric estimator for probability density function is proposed. The TM estimation method is completely different from the existent density estimation methods in that the estimator depends on an approximate system with poles in a complex plane. Compared with the classic Fourier estimator, the TM estimator will offer more flexibility and adaptivity for real data due to the poles and nonlinearity of the phase of TM system. We compare the TM estimator with kernel, wavelet, and spline estimators by simulations. It shows that the introduced TM estimator is a more promising method than the existing and commonly used methods. Copyright © 2016 John Wiley & Sons, Ltd.