Package {LMDT}

Local Manifold Dispersion Test for Heteroskedasticity

Description

Implements the Local Manifold Dispersion Test (LMDT) for detecting complex, non-linear, and high-dimensional heteroskedasticity in linear regression models. LMDT measures the graph-spectral Dirichlet energy of robust log-dispersion residuals over a self-tuning k-nearest neighbors normalized graph Laplacian.

Details

The primary user function is lmdt_test, which supports both formula and matrix interfaces.

Author(s)

Ahmed Sattar Jabbar ahmed.state.me@gmail.com

References

Jabbar, A. S. (2026). The Local Manifold Dispersion Test: A Nonparametric Graph-Spectral Approach for Detecting Complex and High-Dimensional Heteroskedasticity. Working Paper.

Self-Tuning Manifold Graph Construction

Description

Constructs an undirected, self-tuning k-nearest neighbors affinity graph and its normalized Laplacian matrix from a covariate matrix.

Usage

lmdt_graph(X, k = NULL)

Arguments

Value

A list containing matrices W, S, L, local scales sigma, and vertex degrees.

Examples

set.seed(42)
X <- matrix(rnorm(50 * 2), ncol = 2)
g <- lmdt_graph(X, k = 5)
dim(g$S)

Supervised Metric Learning for Sparse Noise Dilution

Description

Computes correlation-based feature weights to soft-threshold uninformative ambient noise coordinates.

Usage

lmdt_metric(X, u, lambda = 0.15)

Arguments

Value

A rescaled covariate matrix with filtered noise dimensions.

Examples

set.seed(42)
X <- matrix(rnorm(50 * 10), nrow = 50, ncol = 10)
u <- rnorm(50)
X_rescaled <- lmdt_metric(X, u, lambda = 0.15)
dim(X_rescaled)

Gavish–Donoho Optimal Adaptive PCA Denoising

Description

Filters high-dimensional correlated features by hard-thresholding singular values at the Gavish–Donoho (2014) optimal threshold.

Usage

lmdt_pca(X)

Arguments

Value

A matrix of retained principal components.

Examples

set.seed(42)
X <- matrix(rnorm(100 * 20), nrow = 100, ncol = 20)
X_clean <- lmdt_pca(X)
ncol(X_clean)

Local Manifold Dispersion Test for Heteroskedasticity

Description

Performs the Local Manifold Dispersion Test (LMDT) for regression heteroskedasticity.

Usage

lmdt_test(x, ...)

## S3 method for class 'formula'
lmdt_test(formula, data = list(), ...)

## S3 method for class 'lm'
lmdt_test(x, ...)

## Default S3 method:
lmdt_test(
  x,
  y,
  k = NULL,
  method = c("permutation", "asymptotic", "wild_bootstrap"),
  alternative = c("one.sided", "two.sided"),
  denoise = c("none", "pca", "metric"),
  B = 499L,
  c = 1e-04,
  lambda = 0.15,
  ...
)

Arguments

Value

An object of class "lmdt" and "htest".

References

Jabbar, A. S. (2026). The Local Manifold Dispersion Test: A Nonparametric Graph-Spectral Approach for Detecting Complex and High-Dimensional Heteroskedasticity. Working Paper.

Examples

set.seed(42)
n <- 100
x1 <- rnorm(n)
x2 <- rnorm(n)
e <- rnorm(n, sd = exp(0.5 * x1))
y <- 1 + 2 * x1 + 3 * x2 + e
fit <- lm(y ~ x1 + x2)

# Using formula interface with asymptotic calibration
test_asymp <- lmdt_test(y ~ x1 + x2, method = "asymptotic")
print(test_asymp)


# Using Wild Bootstrap calibration
test_boot <- lmdt_test(y ~ x1 + x2, method = "wild_bootstrap", B = 199)
print(test_boot)

Plot Diagnostic Visualizations for LMDT

Description

Produces diagnostic plots displaying the null distribution of the test statistic (under bootstrap/permutation or asymptotic Gaussian) and the ordered log-dispersion profile.

Usage

## S3 method for class 'lmdt'
plot(x, ...)

Arguments

Value

Invisibly returns x.

Examples

set.seed(42)
fit <- lm(rnorm(50) ~ matrix(rnorm(100), 50, 2))
res <- lmdt_test(fit, method = "asymptotic")
plot(res)

Methods for LMDT Test Results

Description

Print and summary methods for objects of class "lmdt".

Usage

## S3 method for class 'lmdt'
print(x, digits = 4, ...)

## S3 method for class 'lmdt'
summary(object, ...)

Arguments

Value

Invisibly returns the input object.