This function calculates critical values for the partial-sum and worst-case
statistics.
Usage
getcv(alpha = 0.05, method = "ps", eta = 0.5, simul = 0)
Value
a real number.
Arguments
alpha
a number in \((0,1)\), indicating the significance level of
the test.
method
``ps'' for the partial-sum staistic, others for the worst-case
statistic.
eta
a number in \([0,1]\), a scaling parameter required for "ps"
method; see more details in He et al. (2021).
simul
logical value, woking only for "ps" method with
\(\eta\) not equal to 0.5. When simul is true, the
function will return approximated critical values based on 50000
replications of simulated Wiener process on a grid of 10000 points in
\([0,1]\). Otherwise, the function first checks for the nearest pair of
\((\eta,\alpha)\) in the preserved cv.table, and
then returns the corresponding critical value.
Author
Yong He, Xinbing Kong, Lorenzo Trapani, Long Yu
Details
For the partial-sum statistic with \(\eta=0.5\) or the worst-case
statistic, the critical value is simply \(-log(-log(1-alpha))\). For the
partial-sum statistic with \(\eta\) not equal to 0.5, the critical
value of the scaled Wiener process is approximated by simulated data or from
our preserved table cv.table, covering \(\eta\) in
\([0.01,0.49]\) with step size equal to 0.01 and \(\alpha\) in
\([0.001,0.500]\) with step size equal to 0.001. See more details for the
test statistics in He et al. (2021).
References
He Y, Kong X, Trapani L, & Yu L(2021). Online change-point
detection for matrix-valued time series with latent two-way factor
structure. arXiv preprint, arXiv:2112.13479.