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Estimating Thresholding Levels for Random Fields via Euler Characteristics
 

Summary: Estimating Thresholding Levels for Random Fields via
Euler Characteristics
Kevin Bartz
Department of Statistics
Harvard University
S. C. Kou
Department of Statistics
Harvard University
Robert J. Adler
Faculty of Electrical Engineering
Technion-Israel Institute of Technology
August 2011
Abstract
We introduce Lipschitz-Killing curvature (LKC) regression, a new method to produce accu-
rate 95% and general 1 - thresholds for signal detection in random fields. The method does
not assume knowledge of the covariance function. It works by fitting the observed pattern of the
Euler characteristics of the field to the Gaussian kinematic formula via generalized least squares.
The coefficients are estimates of the LKCs, which can be employed through the Euler character-
istic approximation to generate 1 - thresholds. The proposed method is easy to implement,
transparent to understand and simple to diagnose. We demonstrate that the LKC regression

  

Source: Adler, Robert J. - Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology

 

Collections: Mathematics; Engineering