Outlier detection and robust regression through an iterative penalized regression with tuning parameter chosen by modified BIC
IPOD(X, Y, H, method = "hard", TOL = 1e-04, length.out = 50)an N by k design matrix
an N by 1 response
an N by N projection matrix X(X'X)^{-1}X'
a string, if method = "hard", hard thresholding is applied; if method = "soft", soft thresholding is applied
relative iterative converence tolerance, default to 1e-04
A numeric, number of candidate tuning parameter lambda under consideration for further modified BIC model selection, default to 50.
a vector of length N, estimated outlier indicator gamma
a vector of length N, test statistics for each of the N genes
a vector of length N, p-values for each of the N genes
%% ~Describe the value returned %% If it is a LIST, use %% \item{comp1 }{Description of 'comp1'} %% \item{comp2 }{Description of 'comp2'} %% ...
If there is no predictors, set X = NULL.
Y = X beta + gamma + sigma epsilon
Y is N by 1 reponse vector, X is N by k design matrix, beta is k by 1 coefficients, gamma is N by 1 outlier indicator, sigma is a scalar and the noise standard deviation and epsilon is N by 1 vector with components independently distributed as standard normal N(0,1).