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