Wavelet and Isotonic Regression,

Abstract

Consider the model:y sub i = f(t sub i) + Z sub i where f is a decreasing function 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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1992
Accession Number
ADA298837

Entities

People

  • Hong-ye Gao

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Communities of Interest

  • Materials and Manufacturing Processes

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Fields of Study

  • Mathematics

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  • Computer Vision.
  • Statistical inference.