TFORGE (version 0.1.16)

test_unconstrained: Pivotal bootstrap test of mean eigenvalues

Description

For a single sample of symmetric matrices, test eigenvalues of the population mean. For multiple samples of symmetric matrices, test for equality of the eigenvalues of the population means. Eigenvalues must be distinct.

Usage

test_unconstrained(x, evals = NULL, evecs = NULL, B = 1000)
stat_unconstrained(x, evals = NULL, evecs = NULL)
translate_evalsofav(x, evals)

Value

A TFORGE object (see boot_calib() or chisq_calib()) with the eigenvalues of the null hypothesis in the null_evals attribute for t0.

Arguments

x

A single sample of symmetric matrices or multiple samples of symmetric matrices. See as_flat().

evals

When x is a single sample, the null hypothesis is that the (extrinsic) mean of the population has eigenvalues equal to evals. For multiple samples evals must be omitted.

evecs

For a single sample, specify eigenvectors to test under the assumption that the population mean's eigenvectors are the columns of evecs. The order of these eigenvectors matters and should be such that eigenvalues are in descending order.

B

Number of bootstrap samples. If B = 'chisq' then a chi-squared calibration is used instead.

Hypotheses

For a single sample the null hypothesis is that the population (extrinsic) mean has eigenvalues of evals; the alternative hypothesis is that the eigenvalues are not equal to evals. For multiple samples, evals must be omitted and the null hypothesis is that the population (extrinsic) means have the same eigenvalues.

Details

Test hypotheses described below. For a single sample, the eigenvectors of the population mean in the null and alternative hypotheses may be prespecified by evecs.

Bootstrap resampling is conducted from a population that satisfies the null hypothesis by translating each sample in x with translate_evalsofav() to so that the sample average has the null eigenvalues. The test statistic is calculated by stat_unconstrained().

Examples

test_unconstrained(rsymm_norm(15, diag(c(3,2,1))), evals = c(3, 2, 1), B = 100)
test_unconstrained(list(rsymm_norm(15, diag(c(3,2,1))),
                        rsymm_norm(15, diag(c(3,2,1)))), B = 100)