Independent_transformation: Transformation to Independent Univariate Sample

In PlotNormTest: Graphical Univariate/Multivariate Assessments for Normality Assumption

Transformation to Independent Univariate Sample

Description

Leave-one-out method gives approximately independent sample of standard multivariate normal distribution, which then produces sample of standard univariate normal distribution.

Usage

Multi.to.Uni(x)

Arguments

x	multivariate data matrix

Details

Let \bar{X}_{-k} and S_{-k} are the sample mean sample variance covariance matrix obtained by using all but k^{th} data point. Then S_{-k}^{-1/2} (X_k - \bar{X}_{-k}) , k = 1,... n are approximately independently distributed as N_p(0, I). Thus all n \times p entries in the data matrix so constructed can be treated as univariate samples of size n \times p from N(0, 1).

Value

Data frame contains univariate data and the index from multivariate data.

Examples

set.seed(1)
x <- MASS::mvrnorm(100, mu = rep(0, 5), diag(5))
df <- Multi.to.Uni(x)
qqnorm(df$x.new); abline(0, 1)

PlotNormTest documentation built on April 12, 2025, 9:14 a.m.