irdc_simple: Simple Estimator of the Integrated R-squared Dependence...

In FORD: Feature Ordering by Integrated R Square Dependence

Simple Estimator of the Integrated R-squared Dependence Coefficient (irdc_simple) for 1 Dimensional continuous X and Y

Description

The Simple Integrated R-squared Dependence Coefficient (irdc_simple) is a measure of dependence between a continuous random variables Y and X, based on an i.i.d. sample of (Y, X). The estimated coefficient is asymptotically guaranteed to lie between 0 and 1. The measure is asymmetrical; that is, irdc_simple(X, Y) != irdc_simple(Y, X). The measure equals 0 if and only if X is independent of Y, and it equals 1 if and only if Y is a measurable function of X. This coefficient has several applications; for example, it can be used for independence test. This coefficient only implemented for the 1-Dimensional continuous random variable X and Y.

Usage

irdc_simple(Y, X, na.rm = TRUE)

Arguments

Y	A vector of length n.
X	A vector of length n.
na.rm	Logical; if TRUE, missing values (NAs) will be removed. Default is TRUE.

Details

The value returned by 'irdc_simple' can be positive or negative for finite samples, but asymptotically, it is guaranteed to be between 0 and 1. A small value indicates low dependence between Y and X, while a high value indicates strong dependence. The 'irdc_simple' function is used for testing the independence of variables.

Value

The Simple Integrated R-squared Dependence Coefficient (irdc_simple) between Y and X.

Author(s)

Mona Azadkia, Pouya Roudaki

References

Azadkia, M. and Roudaki, P. (2025). A New Measure Of Dependence: Integrated R2 http://arxiv.org/abs/2505.18146.

See Also

irdc, codec, xicor, KPCgraph, KPCRKHS

Examples

n = 1000
x <- matrix(runif(n * 3), nrow = n)
y <- (x[, 1] + x[, 2])
irdc_simple(y, x[, 1])
irdc_simple(y, x[, 2])
irdc_simple(y, x[, 3])

FORD documentation built on June 8, 2025, 10:03 a.m.