MTElasso | R Documentation |

MTELasso is the penalized MTE for robust estimation and variable selection for linear regression. It can deal with both fixed and high-dimensional settings.

```
MTElasso(
X,
y,
beta.ini,
p = 2,
lambda = NULL,
adaptive = TRUE,
t = 0.01,
intercept = TRUE,
penalty.factor = rep(1, ncol(X)),
...
)
```

`X` |
design matrix, standardization is recommended. |

`y` |
response vector. |

`beta.ini` |
initial estimates of beta. If not specified, LADLasso estimates from |

`p` |
Taylor expansion order. |

`lambda` |
regularization parameter for LASSO, but not necessary if "adaptive=TRUE". |

`adaptive` |
logic argument to indicate if Adaptive-Lasso is used. Default is TRUE. |

`t` |
the tuning parameter that controls for the tradeoff between robustness and efficiency. Default is t=0.01. |

`intercept` |
logical input that indicates if intercept needs to be estimated. Default is FALSE. |

`penalty.factor` |
can be used to force nonzero coefficients. Default is rep(1, ncol(X)) as in glmnet. |

`...` |
other arguments that are used in |

It returns a sparse vector of estimates of linear regression. It has two types of penalty, LASSO and AdaLasso. Coordinate descent algorithm is used for iteratively updating coefficients.

`beta` |
sparse regression coefficient |

`fitted` |
predicted response |

```
set.seed(2017)
n=200; d=500
X=matrix(rnorm(n*d), nrow=n, ncol=d)
beta=c(rep(2,6), rep(0, d-6))
y=X%*%beta+c(rnorm(150), rnorm(30,10,10), rnorm(20,0,100))
output.MTELasso=MTElasso(X, y, p=2, t=0.01)
beta.est=output.MTELasso$beta
```

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