getcv {OLCPM}

calculate critical values

Description

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)

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.

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).

Value

a real number.

Author(s)

Yong He, Xinbing Kong, Lorenzo Trapani, Long Yu

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.

Examples

## Not run: 
getcv(0.05,method="ps",eta=0.25)
getcv(0.05,method="ps",eta=0.25,simul=1)
getcv(0.10,method="wc")

## End(Not run)