CBPE (version 0.1.0)

CBPLinearE: Correlation-based Estimator for Linear Regression Models

Description

This function computes the correlation-based estimator for linear regression models.

Usage

CBPLinearE(X, y, lambda)

Value

A numeric vector of the estimated coefficients for the specified model.

Arguments

X

A numeric matrix of predictors where rows represent observations and columns represent variables.

y

A numeric vector of response variables.

lambda

A regularization parameter.

Details

The correlation-based penalized linear estimator is calculated as: $$ \hat{\beta} = \text{argmin} \left\{ \sum_{i=1}^n (y_i - \mathbf{x}_i^\top \boldsymbol{\beta})^2 + \lambda \sum_{i=1}^{p-1} \sum_{j>i} \left( \frac{(\beta_i - \beta_j)^2}{1 - \rho_{ij}} + \frac{(\beta_i + \beta_j)^2}{1 + \rho_{ij}} \right) \right\} $$ where \(\rho_{ij}\) denotes the (empirical) correlation between the \(i\)th and the \(j\)th predictor.

References

Tutz, G., Ulbricht, J. (2009). Penalized regression with correlation-based penalty. Stat Comput 19, 239–253.

Examples

set.seed(42)
n <- 100
p <- 4
X <- matrix(rnorm(n * p), n, p)
beta_true <- c(0.5, -1, 2, 5)
y <- X %*% beta_true + rnorm(n)
lambda <- 0.1

result <- CBPLinearE(X, y, lambda = lambda)
print(result)