vvtz: Projectin operator

In plsdof: Degrees of Freedom and Statistical Inference for Partial Least Squares Regression

Projectin operator

Description

This function computes the projection operator

P_V z= V V^\top z

Usage

vvtz(v, z)

Arguments

v	orthonormal basis of the space on which z is projected. v is either a matrix or a vector.
z	vector that is projected onto the columns of v

Details

The above formula is only valid if the columns of v are normalized and mutually orthogonal.

Value

value of the projection operator

Author(s)

Nicole Kraemer

See Also

dvvtz

Examples

# generate random orthogonal vectors
X<-matrix(rnorm(10*100),ncol=10) 	# random data
S<-cor(X) 				# correlation matrix of data
v<-eigen(S)$vectors[,1:3]		# first three eigenvectors of correlation matrix
z<-rnorm(10)				# random vector z
projection.z<-vvtz(v,z)

plsdof documentation built on Dec. 1, 2022, 1:13 a.m.