| Type: | Package |
| Title: | General Linear Hypothesis Tests via Spectral Shrinkage |
| Version: | 0.1.0 |
| Contact: | Haoran Li <haoranli1990@gmail.com> (secondary email) |
| Description: | Implements high-dimensional general linear hypothesis tests using ridge, reciprocal cubic polynomial, and user-defined analytic spectral regularizers. Provides prior-based shrinkage selection and Gaussian maximum calibration for composite tests. Implements the methods of Li, Aue and Paul (2020), "High-dimensional general linear hypothesis tests via non-linear spectral shrinkage", Bernoulli, 26(4), 2541-2571 <doi:10.3150/19-BEJ1186>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| Imports: | stats |
| NeedsCompilation: | no |
| Packaged: | 2026-10-17 22:07:23 UTC; haoranli |
| Author: | Haoran Li [aut, cre] |
| Maintainer: | Haoran Li <hzl0152@auburn.edu> |
| Repository: | CRAN |
| Date/Publication: | 2026-10-27 18:40:08 UTC |
General Linear Hypothesis Tests via Spectral Shrinkage
Description
Implements the methods of Li, Aue and Paul (2020), including ridge, reciprocal cubic polynomial, and general analytic regularization.
Details
P-values use asymptotic approximations. A small Gaussian MANOVA study found mild finite-sample LH size inflation; see the package README and installed VALIDATION.md for the design and results. General analytic functions require an admissible contour and numerical convergence checks.
References
Li, H., Aue, A. and Paul, D. (2020). High-dimensional general linear hypothesis tests via non-linear spectral shrinkage. Bernoulli, 26(4), 2541–2571. doi:10.3150/19-BEJ1186.
See Also
glh_test, shrinkage_moments, cubic_grid
Generate a cubic coefficient search grid
Description
Generate a cubic coefficient search grid
Usage
cubic_grid(eigenvalues, resolution = 5L)
Arguments
eigenvalues |
Residual covariance eigenvalues, including zeros. |
resolution |
Number of grid points per dimension (at least two). |
Value
Matrix with columns l0,l1,l2,l3 satisfying the supplementary material's monotonicity and discriminant restrictions.
References
Li, H., Aue, A. and Paul, D. (2020). High-dimensional general linear hypothesis tests via non-linear spectral shrinkage. Bernoulli, 26(4), 2541–2571. doi:10.3150/19-BEJ1186.
Spectral shrinkage general linear hypothesis test
Description
Tests BC = 0 in Y = BX + error. Columns of Y are observations. Selection maximizes the estimated local power numerator divided by the square root of the estimated variance on a finite candidate grid.
Usage
glh_test(Y, X, C, family = c("linear", "cubic", "general"),
mode = c("single", "composite"), prior = c(1, 0, 0),
priors = diag(3), parameters = NULL, regularizer = NULL,
contour = NULL, nquad = 256L, nsim = 10000L, alpha = 0.05)
Arguments
Y |
Numeric p by N response matrix. |
X |
Numeric k by N full row rank design matrix. |
C |
Numeric k by q full column rank contrast matrix. |
family |
One of linear (ridge), cubic (reciprocal polynomial), general. |
mode |
Single prior test or maximum across multiple priors. |
prior |
Nonnegative length-three weights for a single test. |
priors |
Matrix of nonnegative prior rows for a composite test. |
parameters |
Candidate parameters; see shrinkage_moments. Defaults to 60 logarithmically spaced negative ridge parameters or cubic_grid. |
regularizer |
Vectorized function(z, parameter) for general shrinkage. |
contour |
Circular integration contour; see shrinkage_moments. |
nquad |
Contour quadrature node count. |
nsim |
Number of Gaussian simulations for composite calibration. |
alpha |
Significance level. |
Details
Calibration is asymptotic. A small Gaussian MANOVA study found mild finite-sample LH size inflation (up to 7.6 percent at nominal 5 percent). See the package README and installed VALIDATION.md.
Value
A list with statistic, p.value and reject for LR, LH and BNP; component statistics, selected parameters, prior weights, moments, covariance before and after PSD projection, and residual dimensions.
References
Li, H., Aue, A. and Paul, D. (2020). High-dimensional general linear hypothesis tests via non-linear spectral shrinkage. Bernoulli, 26(4), 2541–2571. doi:10.3150/19-BEJ1186.
Examples
set.seed(1)
Y <- matrix(rnorm(10 * 40), 10, 40)
X <- rbind(1, rep(c(0, 1), each = 20))
C <- matrix(c(0, 1), 2, 1)
glh_test(Y, X, C)
glh_test(Y, X, C, mode = "composite", nsim = 1000)
Estimate null moments and prior power numerators
Description
Estimate null moments and prior power numerators
Usage
shrinkage_moments(eigenvalues, gamma,
family = c("linear", "cubic", "general"), parameters,
regularizer = NULL, contour = NULL, nquad = 256L)
Arguments
eigenvalues |
Nonnegative eigenvalues of the residual covariance, including its zero eigenvalues. |
gamma |
Dimension divided by residual degrees of freedom. |
family |
One of linear, cubic, general. |
parameters |
Negative ridge parameters; cubic coefficient matrix with columns l0,l1,l2,l3; or matrix of user-defined parameter rows. |
regularizer |
Vectorized function(z, parameter) supporting complex z. |
contour |
List with center and radius for a counterclockwise circle. Must enclose the empirical spectrum and kernel singularities, but no singularities of the regularizers. Required for the general family. |
nquad |
Number of equally spaced midpoint contour nodes. |
Value
List containing omega, delta, numerator (three prior basis columns), parameters, and complex numerical estimates for the general family.
References
Li, H., Aue, A. and Paul, D. (2020). High-dimensional general linear hypothesis tests via non-linear spectral shrinkage. Bernoulli, 26(4), 2541–2571. doi:10.3150/19-BEJ1186.