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Let Y:{-1, 1} be a binary variable Y and consider its prediction from a variable X: →R. Prove that the Bayes predictors for the 0/1 loss function r(y, y) = 1yty and for the quadratic loss r(y, y) = (y - y)² coincide.

Let Y:{-1, 1} be a binary variable Y and consider its prediction from a variable X: →R. Prove that the Bayes predictors for the 0/1 loss function r(y, y) = 1yty and for the quadratic loss r(y, y) = (y - y)² coincide.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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Let Y : N { 1,1} be a binary variable Y and consider its prediction from a variable X: N - R. Prove that the Bayes predictors for the 0/1 loss function r(y, y) 1yy and for the quadr atic loss r(y, y) = (y-y) coincide.
Transcribed Image Text:Let Y : N { 1,1} be a binary variable Y and consider its prediction from a variable X: N - R. Prove that the Bayes predictors for the 0/1 loss function r(y, y) 1yy and for the quadr atic loss r(y, y) = (y-y) coincide.
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