Pilliat_test {HDCD}

Pilliat single change-point test

Description

R wrapper function testing for a single change-point using the three test statistics in the multiple change point detection algorithm of Pilliat et al. (2023). See also Appendix E in Moen et al. (2023).

Usage

Pilliat_test(
  X,
  empirical = FALSE,
  N = 100,
  tol = 0.05,
  thresholds_partial = NULL,
  threshold_dense = NULL,
  thresholds_bj = NULL,
  threshold_d_const = 4,
  threshold_bj_const = 6,
  threshold_partial_const = 4,
  rescale_variance = TRUE,
  fast = FALSE,
  debug = FALSE
)

Arguments

X

Matrix of observations, where each row contains a time series

empirical

If TRUE, detection thresholds are based on Monte Carlo simulation

N

If empirical=TRUE, N is the number of Monte Carlo samples used

tol

If empirical=TRUE, tol is the false error probability tolerance

thresholds_partial

Vector of manually specified detection thresholds for the partial sum statistic, for sparsities/partial sums t=1,2,4,\ldots,2^{\lfloor\log_2(p)\rfloor}

threshold_dense

Manually specified value of detection threshold for the dense statistic

thresholds_bj

Vector of manually specified detection thresholds for the Berk-Jones statistic, order corresponding to x=1,2,\ldots,x_0

threshold_d_const

Leading constant for the analytical detection threshold for the dense statistic

threshold_bj_const

Leading constant for p_0 when computing the detection threshold for the Berk-Jones statistic

threshold_partial_const

Leading constant for the analytical detection threshold for the partial sum statistic

rescale_variance

If TRUE, each row of the data is re-scaled by a MAD estimate (see rescale_variance)

fast

If TRUE, only the mid-point of (0,\ldots,n] is tested for a change-point. Otherwise a test is performed at each candidate change-point poisition

debug

If TRUE, diagnostic prints are provided during execution

Value

1 if a change-point is detected, 0 otherwise

References

Moen PAJ, Glad IK, Tveten M (2023). “Efficient sparsity adaptive changepoint estimation.” Arxiv preprint, 2306.04702, https://doi.org/10.48550/arXiv.2306.04702.

Pilliat E, Carpentier A, Verzelen N (2023). “Optimal multiple change-point detection for high-dimensional data.” Electronic Journal of Statistics, 17(1), 1240 – 1315.

Examples

library(HDCD)
n = 200
p = 200

# Generating data
X = matrix(rnorm(n*p), ncol = n, nrow=p)
Y = matrix(rnorm(n*p), ncol = n, nrow=p)

# Adding a single sparse change-point to X (and not Y):
X[1:5, 100:200] = X[1:5, 100:200] +1

# Vanilla Pilliat test:
resX = Pilliat_test(X)
resX
resY = Pilliat_test(Y)
resY

# Manually setting leading constants for the theoretical thresholds for the three 
# test statistics used
resX = Pilliat_test(X, 
                    threshold_d_const=4, 
                    threshold_bj_const=6, 
                    threshold_partial_const=4
)
resX 
resY = Pilliat_test(Y, 
                    threshold_d_const=4, 
                    threshold_bj_const=6, 
                    threshold_partial_const=4
)
resY

# Empirical choice of thresholds:
resX = Pilliat_test(X, empirical = TRUE, N = 100, tol = 1/100)
resX
resY = Pilliat_test(Y, empirical = TRUE, N = 100, tol = 1/100)
resY

# Manual empirical choice of thresholds (equivalent to the above)
thresholds_test_emp = Pilliat_test_calibrate(n,p, N=100, tol=1/100,bonferroni=TRUE)
resX = Pilliat_test(X, 
                    threshold_dense=thresholds_test_emp$threshold_dense, 
                    thresholds_bj = thresholds_test_emp$thresholds_bj, 
                    thresholds_partial = thresholds_test_emp$thresholds_partial
)
resX
resY = Pilliat_test(Y, 
                    threshold_dense=thresholds_test_emp$threshold_dense, 
                    thresholds_bj = thresholds_test_emp$thresholds_bj, 
                    thresholds_partial = thresholds_test_emp$thresholds_partial
)
resY