Nonparametric Estimation Using Wavelet Tensor and Hyperbolic Wavelets with Fractional Gaussian Fields

• Activity Number: 260
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Justin Wishart*
• Companies: Macquarie University
• Keywords: Wavelet analysis ; Fourier Analysis ; Multivariate functions ; Nonparametric regression

Abstract

The estimation of multivariate nonparametric functions of general dimension, $d \ge 2$, is considered using either the standard wavelet-tensor basis and the hyperbolic wavelet basis. In particular the performance of both methods is measured with the $L_p$ loss when the functions are observed in noise modelled by fractional Brownian sheets. The hyperbolic basis is shown to be a superior for estimation, capturing possible anisotropy in functions and the noise process.