confelps {lmreg}

Confidence ellipsiod for multiple parameters in a linear model.

Description

Computes confidence ellipsiod for a vector of estimable functions in a linear model.

Usage

confelps(y, X, A, alpha, tol=sqrt(.Machine$double.eps))

Arguments

y

Responese vector in linear model.

X

Design/model matrix or matrix containing values of explanatory variables (generally including intercept).

A

Coefficient matrix (A.beta is the vector for which confidence interval is needed).

alpha

The non-coverage probability of confidence ellipsoid.

tol

A relative tolerance to detect zero singular values while computing generalized inverse, in case X is rank deficient (default = sqrt(.Machine$double.eps)).

Details

Normal distribution of response (given explanatory variables and/or factors) is assumed.

Value

Returns a list of three objects:

CenterOfEllipse

Center of ellipsoid.

MatrixOfEllipse

Matrix of ellipsoid, for describing quadratic form in terms of the vector of deviations from center of ellipsoid.

threshold

Upper limit of quadratic form that completes specification of ellipsoid.

Author(s)

Debasis Sengupta <[e-mail]>, Jinwen Qiu <[e-mail]>

References

Sengupta and Jammalamadaka (2019), Linear Models and Regression with R: An Integrated Approach.

Examples

data(denim)
attach(denim)
X <- cbind(1,binaries(Denim),binaries(Laundry))
A <- rbind(c(0,1,0,-1,0,0,0),c(0,0,1,-1,0,0,0))
confelps(Abrasion, X, A, 0.05,tol=1e-12)
detach(denim)