mram {MRAM}R Documentation

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 n \times d matrix of responses.

x_data

A n \times p Matrix of predictors.

z_data

A n \times q matrix of conditional predictors.

bootstrap

Perform the m-out-of-n bootstrap if TRUE. The default value is FALSE.

B

Number of bootstrap replications. The default value is 1000.

g_vec

A vector used to generate a collection of rules for the m-out-of-n bootstrap. The default value is seq(0.4,0.9,by = 0.05).

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 m generated by g_vec.

T_se_vec

The vector of standard error estimates obtained from the m-out-of-n bootstrap, where m is equal to m_vec.

J_cluster

The index of the best m_vec chosen by the cluster rule.

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

vs_mram

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)

[Package MRAM version 0.1.2 Index]