test.once.psi.robust {OLCPM}

robust test of single change point for matrix-valued online data given rolling eigenvalue series

Description

Based on test.once.psi, this function repeats the randomized procedure multiple times and reports the majority vote, thus more robust.

Usage

test.once.psi.robust(
  m = 20,
  psi,
  method = "ps",
  eta = 0.25,
  cv = 2.386,
  S = 100,
  pr = 0.75
)

Arguments

m

a positive integer (>1) indicating the bandwidth of the rolling windom.

psi

the transformed eigenvalue series, produced by gen.psi.tau.flat or gen.psi.tau.proj, with length T-m.

method

indicating the test statistic, “ps” for the partial-sum method, while others for the worst-case method.

eta

a number between [0,1), indicating the parameter \eta used in the partial-sum statistic.

cv

critical value; see also test.once.psi.

S

an integer indicating the number of replications.

pr

an number in (0,1]). The procedure reports a change point only when the proportion of positive votes is over pr in the S replications.

Details

See He et al. (2021).

Value

a list containing:

test

a logical value. 1 indicating the existence of change point, 0 indicating no change point.

loc

an integer larger than m, indicating the median location of the change point among the positive votes in the S replications; or NA when no change point is reported.

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

k1=3
k2=3
epsilon=0.05
Sample_T=50
p1=40
p2=20
kmax=8
r=8
m=p2

# generate data
Y=gen.data(Sample_T,p1,p2,k1,k2,tau=0.5,change=1,pp=0.5)

# calculate delta
temp=log(p1)/log(m*p2)
delta=epsilon*(temp<=0.5)+(epsilon+1-1/(2*temp))*(temp>0.5)

# calculate psi.tau
psi1=gen.psi.tau.proj(Y,k1+1,m,delta,r,kmax)
psi2=gen.psi.tau.flat(Y,k1+1,m,delta,r)

# calculate cv for "ps" with eta=0.45 and "wc"
cv1=getcv(0.05,method="ps",eta=0.45)
cv2=getcv(0.05,method="wc")


# test with psi1
test.once.psi.robust(m,psi1[,3],method="ps",eta=0.45,cv1,S=100,pr=0.75)

test.once.psi.robust(m,psi1[,3],method="wc",eta=0.5,cv2,S=100,pr=0.75)


# test with psi2
test.once.psi.robust(m,psi2[,3],method="ps",eta=0.45,cv1,S=100,pr=0.75)

test.once.psi.robust(m,psi2[,3],method="wc",eta=0.5,cv2,S=100,pr=0.75)