In liyi-1989/rcd: Robust Copula Dependence

In this vignette, we demonstrate how to use a new R package rcd for implementing the robust copula dependence (RCD).

1. The Robust Copula Dependence

RCD is a dependence measure which is designed for detecting nonlinear relationship among the data. Specifically, let $X$ and $Y$ be two random variables, and $U= F_X(X), V= F_Y(Y)$, where $F_X$ and $F_Y$ are the CDFs of $X$ and $Y$. The copula density for the joint random variable $(U, V)$ is denoted by $c(u,v)$. The copula distance between $X$ and $Y$ is

[ CD_{\alpha}=\frac{1}{2}\int!!\int_{I^2}|c(u,v)-1|^{\alpha}du dv, \quad \alpha>0. ]

In particular, we call $CD_1$ the robust copula dependence and denote it by RCD.

2. The Estimation Methods

The main function rcd in the rcd is used to estimate the RCD between two random variables. Two estimation methods are available for the RCD estimation, the kernel density estimation based method (kde), and the K-nearest-neighbour based method (knn).

These two methods could be specified with the method = argument of the rcd function. Each of the estimation method comes with a tuning parameter. The bandwidth bandwidth for method = "kde" and k for method = "knn". However, they are already set to their default values.

3. Code Example

require(rcd)
n <- 1000
x <- runif(n)
y <-  x^2 + 2*runif(n)
res.kde <- rcd(x, y, method = "kde")

liyi-1989/rcd documentation built on May 21, 2019, 7:32 a.m.