Description Usage Arguments Details Value Author(s) References

Y = X beta + gamma + sigma epsilon estimate k by 1 coefficients vector beta and N by 1 outlier indicator vector gamma from (Y,X).

1 |

`X` |
an N by k design matrix |

`Y` |
an N by 1 response vector |

`H` |
an N by N projection matrix X(X'X)^-1X' |

`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 |

The initial estimator for the coefficient beta can be chosen to be the estimator from a robust linear regression

`gamma ` |
an N by 1 vector of estimated outlier indicator |

`ress` |
an N by 1 vector of residual Y - X beta - gamma |

Yunting Sun yunting.sun@gmail.com, Nancy R.Zhang nzhang@stanford.edu, Art B.Owen owen@stanford.edu

She, Y. and Owen, A.B. "Outlier detection using nonconvex penalized regression" 2010

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