PM.matrix: Partial Moment Matrix

In NNS: Nonlinear Nonparametric Statistics

Partial Moment Matrix

Description

Builds a list containing CUPM, DUPM, DLPM, CLPM and the overall covariance matrix.

Usage

PM.matrix(LPM_degree, UPM_degree, target, variable, pop_adj, norm = FALSE)

Arguments

LPM_degree	numeric; lower partial moment degree (0 = freq, 1 = area).
UPM_degree	numeric; upper partial moment degree (0 = freq, 1 = area).
target	numeric vector; thresholds for each column (defaults to colMeans).
variable	numeric matrix or data.frame.
pop_adj	logical; TRUE adjusts population vs. sample moments.
norm	logical; default FALSE. If TRUE, each quadrant matrix is cell-wise normalized so their sum is 1 at each (i,j).

Details

Partial Moment Matrix

Value

A list: $cupm, $dupm, $dlpm, $clpm, $cov.matrix.

Note

When norm = TRUE, each cell (i,j) of the four quadrant matrices is normalized so that their sum equals 1. In this case, $cov.matrix is computed as $cupm + $clpm - $dupm - $dlpm, yielding a dimensionless, signed dependence measure bounded between -1 and 1. This representation discards magnitude information and is therefore a lossy nonlinear correlation matrix. A higher fidelity nonlinear correlation matrix is available via the NNS.dep function.

Examples

set.seed(123)
A <- cbind(rnorm(100), rnorm(100), rnorm(100))

# Uses norm = FALSE by default
PM.matrix(1, 1, target = NULL, variable = A, pop_adj = TRUE)

# Enable normalization
PM.matrix(1, 1, target = NULL, variable = A, pop_adj = TRUE, norm = TRUE)

# Use 0's for targets
PM.matrix(1, 1, target = rep(0, ncol(A)), variable = A, pop_adj = TRUE)        

# Use variable medians as targets
PM.matrix(1, 1, target = apply(A, 2, "median"), variable = A, pop_adj = TRUE)  

NNS documentation built on April 10, 2026, 9:10 a.m.