When a 3x3 symmetric matrix has a fixed-trace constraint, the vector of its eigenvalues lies on a 2D plane.
This function calculates the boundary of an approximate confidence region in this 2D plane using the same statistic as test_fixedtrace().
The returned boundary can be used to plot the confidence region.
The function conf_fixedtrace_inregion() returns where given points are in the estimated confidence region.
conf_fixedtrace(x, alpha = 0.05, B = 1000, npts = 1000, check = TRUE)conf_fixedtrace_inregion(evals, cr)
A list:
est: the eigenvalues of the mean matrix.
boundary: A matrix with 3 columns and npts rows giving the boundary of the region. Each row corresponds to a point on the boundary and the columns are the first, second and final eigenvalue.
Omega: The estimated covariance of the (projected) eigenvalues
threshold: The threshold (estimated via resampling) on the statistic.
A single sample of 3x3 symmetric matrices. x must be either an fsm object or something that as_fsm() can parse.
Desired significance level of the approximate confidence region.
Number of bootstrap resamples.
Number of points on the boundary of the region to compute.
If TRUE, then the extrinsic means of 100 new resamples will be used to check the coverage of the region.
A set of eigenvalues with the same trace as matrices in x.
A confidence region returned by conf_fixedtrace().
Uses the same statistic as test_fixedtrace() and bootstrap resampling to obtain approximate bounds on the eigenvalues of a population mean.
The statistic has a quadratic form so that the boundary of the confidence region is an ellipse, but for plotting simplicity the ellipse is returned as a dense set of npts points.
A warning will be generated if the confidence region leaves the space of distinct descending-order eigenvalues and a check of coverage of bootstrap resamples is available.