estimateSigma: Estimate the noise level in linear regression with presence...

In shuxiaoc/outference: Valid Inference in Linear Regression Corrected for Outlier Removal

Description

This function estimates the noise level σ in linear regression with possible presence of outliers, based on "lasso-refitting" strategy.

Usage

estimateSigma(y, X)

Arguments

y,	the response.
X,	the design matrix with the first column being 1 (the column of intercepts).

Details

Assume the mean-shift model

y = X β + u + ε,

where ε ~ N(0, σ^2 I). This is equivalent to

y = X.enlarged β + ε,

where X.enlarged = (X : I_n). This function fits a lasso regression based on (y, X.enlarged) with the cross-validated tuning parameter, and then computes the residual sum of square, scaled by 1/(n-s), where s is the number of active variables estimated by lasso.

Value

This function returns an estimate of the noise level σ.

shuxiaoc/outference documentation built on July 8, 2019, 8:30 p.m.