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 |
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)