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IPODFUN: compute the iterative penalized outlier detection given the noise standard deviation sigma
Description
Y = X beta + gamma + sigma epsilon estimate k by 1 coefficients vector beta and N by 1 outlier indicator vector gamma from (Y,X).
Usage
IPODFUN(X, Y, H, sigma, betaInit, method = "hard", TOL = 1e-04)
Arguments
X
an N by k design matrix
Y
an N by 1 response vector
H
an N by N projection matrix X(X'X)^{-1}X'
sigma
a numeric, noise standard deviation
betaInit
a k by 1 initial value for coeffient beta
method
a string, if "hard", conduct hard thresholding, if "soft", conduct soft thresholding, default to "hard"
TOL
a numeric, tolerance of convergence, default to 1e-04
Value
gamma
an N by 1 vector of estimated outlier indicator
ress
an N by 1 vector of residual Y - X beta - gamma
Details
The initial estimator for the coefficient beta can be chosen to be the estimator from a robust linear regression
References
She, Y. and Owen, A.B. "Outlier detection using nonconvex penalized regression" 2010