Description Usage Arguments Details Value Author(s)

Robust marginal integration procedures for additive models.

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`Xp` |
Matrix of explanatory variables (n by p). |

`yp` |
Vector of responses (missing values are allowed). |

`point` |
Matrix of points where predictions will be computed and returned. |

`windows` |
Vector or a squared matrix of bandwidths for the smoothing estimation procedure. |

`prob` |
Probabilities of observing each response (n). Defaults to “NULL”. |

`sigma.hat` |
Estimate of the residual standard error. If NULL we use the mad of the residuals obtained with local medians. |

`win.sigma` |
Vector of bandwidths for estimating sigma.hat. If NULL it uses the argument windows if it is a vector or its diagonal if it is a matrix. |

`epsilon` |
Convergence criterion. |

`type` |
Three different type of estimators can be selected: type '0' (local constant on all the covariates), type '1' (local linear smoother on all the covariates), type 'alpha' (local polynomial smoother only on the direction of interest). |

`degree` |
Degree of the local polynomial smoother in the direction of interest when using the estimator of type 'alpha'. Defaults to “NULL” for the case when using estimators of type '0' or '1'. |

`typePhi` |
One of either “Tukey” or “Huber”. |

`k.h` |
Tuning constant for a Huber-type loss function. Defaults to “1.345”. |

`k.t` |
Tuning constant for a Tukey-type loss function. Defaults to “4.685”. |

`max.it` |
Maximum number of iterations for the algorithm. |

`qderivate` |
If TRUE, it calculates g^(q+1)/(q+1)! for each component only for the type 'alpha' method. Defaults to “FALSE”. |

`orderkernel` |
Order of the kernel used in the nuisance directions when using the estimator of type 'alpha'. Defaults to “2”. |

`Qmeasure` |
A matrix of points where the integration procedure ocurrs. Defaults to “NULL” for calcuting the integrals over the sample. |

Three types of robust marginal integration procedures for additive models.

`mu ` |
Estimate for the intercept. |

`g.matrix ` |
Matrix of estimated additive components (n by p). |

`sigma.hat ` |
Estimate of the residual standard error. |

`prediction ` |
Matrix of estimated additive components for the points listed in the argument point. |

`mul ` |
A vector of size p showing in each component the estimated intercept that considers only that direction of interest when using the type 'alpha' method. |

`g.derivative ` |
Matrix of estimated derivatives of the additive components (only when qderivate is “TRUE”) (n by p). |

`prediction.derivate ` |
Matrix of estimated derivatives of the additive components for the points listed in the argument point (only when qderivate is “TRUE”). |

`Xp` |
Matrix of explanatory variables. |

`yp` |
Vector of responses. |

Alejandra Martinez, Matias Salibian-Barrera

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