Wavelet and Isotonic Regression

摘要

Consider the model:y sub i = f(t sub i) + Z sub i where f is a decreasingfunction and . Z sub i are assumed to be a stationary Gaussian process with mean zero and variance sigma-sq. We propose a simple thresholding procedure based on the fact that the wavelet coefficients for f, under Haar basis, are non-negative. We show that our estimator is competitive with the Grenander estimator both theoretically and numerically (in the sense of mean square error). Key Words and Phrases: Isotonic Regression; Monotone Curve; Grenander Estimator; Orthogonal Wavelet Transformation; Shrinkage Estimator.