Wavelets for Nonparametric Stochastic Regression with Mixing Stochastic Process

Abstract

We propose a wavelet based stochastic regression function estimator for the estimation of the regression function for a sequence of mixing stochastic process with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator are investigated. It is found that the estimators have similar properties to their counterparts studied earlier in literature.

Keywords:

• Besov space
• Mixing stochastic process
• Multiresolution analysis
• Nonparametric curve estimation
• Random design
• Wavelets

Acknowledgment

Support from Ordered and Spatial Data Center of Excellent of Ferdowsi University of Mashhad is acknowledged.