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

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