# constrInResponseCook: Compute the truncation set in the response after outlier... In shuxiaoc/outference: Valid Inference in Linear Regression Corrected for Outlier Removal

## Description

This function computes the matrices Q_i, such that outlier detection using Cook's distance is equivalent to \bigcap_{i \in [n]} y^T Q_i y ≥ 0.

## Usage

 1 constrInResponseCook(n, p, PX, PXperp, outlier.det, cutoff) 

## Arguments

 n,  the number of observations. p,  the number of variables, including the intercept. PX,  the projection matrix onto the column space of the design matrix X. PXperp,  I - PX. outlier.det,  indexes of detected outliers, can be empty. cutoff,  the cutoff λ (see details).

## Details

Using Cook's distance as a heuristic, the i-th data is considered as an outlier if and only if its Cook's distance is larger than λ/n, where lambda is the user-specified cutoff. Then we can characterize this "detection event" as an intersection of quadratic constraints in the response y by \bigcap_{i \in [n]} y^T Q_i y ≥ 0.

## Value

This function returns a list of matrices Q_i.

shuxiaoc/outference documentation built on Dec. 5, 2017, 3:48 a.m.