Local Manifold Dispersion Test for Heteroskedasticity

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("wild_bootstrap", "permutation", "asymptotic"),
  alternative = c("one.sided", "two.sided"),
  denoise = c("none", "pca", "metric"),
  B = 499L,
  c = 1e-04,
  lambda = 0.15,
  ...
)

Arguments

x

A numeric design matrix of regressors, or a formula.

...

Further arguments passed to methods.

formula

A symbolic regression formula (e.g. y ~ x1 + x2).

data

An optional data frame containing model variables.

y

A numeric vector of regression residuals or response variable.

k

An integer number of nearest neighbors. Default uses adaptive rule of thumb.

method

P-value calibration: "wild_bootstrap" (default), "permutation", or "asymptotic".

alternative

Alternative hypothesis: "one.sided" (smooth manifold variance, default) or "two.sided".

denoise

High-dimensional pre-filtering: "none" (default), "pca", or "metric".

B

Number of bootstrap or permutation replications. Default is 499.

c

Positive stabilizer for log-dispersion transform. Default is 1e-4.

lambda

Shrinkage prior for metric learning. Default is 0.15.

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)
#> 
#>   Local Manifold Dispersion Test (LMDT, asymptotic)
#> 
#> data:  y ~ x1 + x2
#> Z_LMD = 7.8466, T_LMD = 0.7716, p-value = 2.109e-15
#> alternative hypothesis: heteroskedasticity with local manifold smoothness (T_LMD < 1)
#> denoising scheme: none
#> 

# \donttest{
# Using Wild Bootstrap calibration
test_boot <- lmdt_test(y ~ x1 + x2, method = "wild_bootstrap", B = 199)
print(test_boot)
#> 
#>   Local Manifold Dispersion Test (LMDT, wild_bootstrap)
#> 
#> data:  y ~ x1 + x2
#> Z_LMD = 7.8466, T_LMD = 0.7716, p-value = 0.005
#> alternative hypothesis: heteroskedasticity with local manifold smoothness (T_LMD < 1)
#> replications: B = 199, neighborhood size: k = 
#> denoising scheme: none
#> 
# }