| Type: | Package |
| Title: | Multivariate Regression Association Measure |
| Version: | 0.1.2 |
| Description: | The multivariate regression association measure quantifies the predictability of one random vector from another. This package provides a function for estimating and performing inference on this measure. A variable selection algorithm based on this measure is also included. For more details, see Shih and Chen (2025) <in revision>. |
| Depends: | RANN |
| License: | GPL-2 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | no |
| Packaged: | 2025-06-05 02:34:09 UTC; adm |
| Author: | Jia-Han Shih [aut, cre], Yi-Hau Chen [aut] |
| Maintainer: | Jia-Han Shih <jhshih@math.nsysu.edu.tw> |
| Repository: | CRAN |
| Date/Publication: | 2025-06-06 13:20:13 UTC |
Estimate Multivariate Regression Association Measure
Description
Estimate the multivariate regression association measure proposed in Shih and Chen (2025). Standard error estimates are obtained by applying the m-out-of-n bootstrap proposed in Dette and Kroll (2024).
Usage
mram(
y_data,
x_data,
z_data = NULL,
bootstrap = FALSE,
B = 1000,
g_vec = seq(0.4, 0.9, by = 0.05)
)
Arguments
y_data |
A |
x_data |
A |
z_data |
A |
bootstrap |
Perform the |
B |
Number of bootstrap replications. The default value is |
g_vec |
A vector used to generate a collection of rules for the |
Details
The value T_est returned by mram is between -1 and 1. However, it is between 0 and 1 asymptotically. A small value indicates that x_data has low predictability for y_data condition on z_data in the sense of the considered measure. Similarly, a large value indicates that x_data has high predictability for y_data condition on z_data. If z_data = NULL, the returned value indicates the unconditional predictability.
Value
T_est |
The estimate of the multivariate regression association measure. |
T_se_cluster |
The standard error estimate based on the cluster rule. |
m_vec |
The vector of |
T_se_vec |
The vector of standard error estimates obtained from the |
J_cluster |
The index of the best |
References
Dette and Kroll (2024) A Simple Bootstrap for Chatterjee’s Rank Correlation, Biometrika, asae045.
Shih and Chen (2025) Measuring multivariate regression association via spatial sign (in revision, Computational Statistics & Data Analysis)
See Also
Examples
n = 100
lambda_para = 3
sigma_para = 0.4
x_data = matrix(rnorm(n*2),n,2)
y_data = matrix(0,n,2)
y_data[,1] = x_data[,1]+x_data[,2]+lambda_para*sigma_para*rnorm(n)
y_data[,2] = x_data[,1]-x_data[,2]+lambda_para*sigma_para*rnorm(n)
library(MRAM)
res = mram(y_data,x_data,bootstrap = FALSE)
Variable Selection via the Multivariate Regression Association Measure
Description
Perform variable selection via the multivariate regression association measure proposed in Shih and Chen (2025).
Usage
vs_mram(y_data, x_data)
Arguments
y_data |
A |
x_data |
A |
Details
vs_mram is a forward and stepwise variable selection algorithm which utilizes the multivariate regression association measure proposed in Shih and Chen (2025). The Algorithm is modified from the feature ordering by conditional independence (FOCI) algorithm from Azadkia and Chatterjee (2021).
Value
The vector containing the indices of the selected predictors in the order they were chosen.
References
Azadkia and Chatterjee (2021) A simple measure of conditional dependence, Annals of Statistics, 46(6): 3070-3102.
Shih and Chen (2025) Measuring multivariate regression association via spatial sign (in revision, Computational Statistics & Data Analysis)
See Also
Examples
n = 200
p = 10
x_data = matrix(rnorm(p*n),n,p)
y_data = x_data[,1]*x_data[,2]+x_data[,1]-x_data[,3]+rnorm(n)
colnames(x_data) = paste0(rep("X",p),seq(1,p))
library(MRAM)
mram_res = vs_mram(y_data,x_data)