Description Usage Arguments Details Value References

This function computes a matrix *A* and a vector *b*, such that
outlier detection using lasso is equivalent to
*A y ≥ b*.

1 | ```
constrInResponseLasso(n, p, PXperp, outlier.det, outlier.det.sign, cutoff)
``` |

`n, ` |
the number of observations. |

`p, ` |
the number of variables, including the intercept. |

`PXperp, ` |
the projection matrix onto the orthogonal complement
of the column space of the design matrix |

`outlier.det, ` |
indexes of detected outliers, can be empty. |

`outlier.det.sign, ` |
the sign of the active variable estimated by lasso. |

`cutoff, ` |
the cutoff |

Consider solving the following program

*minimize ||y-Xβ-u||_2^2/(2n) + λ ||u||_1.*

The *i*-th observation is considered as an outlier
if and only if *\hat u_i \neq 0*.
This is equivalent to solving

*minimize ||P_X^\perp (y-u)||_2^2/(2n) + λ ||u||_1.*

Then the variable selection can be characterized by a set of affine constraints
*Ay ≥ b*. In essence, this function is equivalent to
`selectiveInference:::fixedLasso.poly`

, but adapted to our notations
and up to some scaling factors and linear transformations.

This function returns a list (A, b).

Lee, Jason D., et al. "Exact post-selection inference, with application to the lasso." The Annals of Statistics 44.3 (2016): 907-927.

Tibshirani, R., et al. "selectiveInference: Tools for Post-Selection Inference." R package version 1.3 (2016).

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