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

## Description

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

## Usage

 1 constrInResponseCookSeq(n, p, PX, PXperp, obs.ordered, numOfOutlier) 

## 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. obs.ordered,  the index of observations with their cook's distance in the decreasing order. numOfOutlier,  the number of outliers assumed, must be between 0 and n.

## Details

Using Cook's distance sequentially and assume there are k outliers, the i-th data is considered as an outlier if and only if its Cook's distance ranks in top-k among all, Then we can characterize this "detection event" as an intersection of quadratic constraints in the response y by \bigcap_{i \in I} y^T Q_i y ≥ 0, where I is a finite index set.

## Value

This function returns a list of matrices Q_i.

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