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

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 July 8, 2019, 8:30 p.m.