confelps: 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)).
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.
Details
Normal distribution of response (given explanatory variables and/or factors) is assumed.
References
Sengupta and Jammalamadaka (2019), Linear Models and Regression with R: An Integrated Approach.
# NOT RUN {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)
# }