Inspect_test {HDCD}

Inspect single change-point test

Description

R wrapper for C function testing for a single change-point using Inspect Wang and Samworth (2018).

Usage

Inspect_test(
  X,
  lambda = NULL,
  xi = NULL,
  eps = 1e-10,
  empirical = FALSE,
  N = 100,
  tol = 1/100,
  maxiter = 10000,
  rescale_variance = TRUE,
  debug = FALSE
)

Arguments

X

Matrix of observations, where each row contains a time series

lambda

Manually specified value of \lambda (can be NULL, in which case \lambda \gets \sqrt{\log(p\log n)/2})

xi

Manually specified value of \xi (can be NULL, in which case \xi \gets 4\sqrt{\log(np)})

eps

Threshold for declaring numerical convergence of the power method

empirical

If TRUE, the detection threshold xi is based on Monte Carlo simulation using Inspect_test_calibrate

N

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

tol

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

maxiter

Maximum number of iterations for the power method

rescale_variance

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

debug

If TRUE, diagnostic prints are provided during execution

Value

1 if a change-point is detected, 0 otherwise

References

Wang T, Samworth RJ (2018). “High dimensional change point estimation via sparse projection.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80(1), 57–83. ISSN 1467-9868, doi:10.1111/rssb.12243, https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssb.12243.

Examples

library(HDCD)
n = 50
p = 50

# 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, 26:n] = X[1:5, 26:n] +1

# Vanilla Inspect:
resX = Inspect_test(X)
resX
resY = Inspect_test(Y)
resY

# Manually setting \lambda and \xi:
resX = Inspect_test(X, 
                    lambda = sqrt(log(p*log(n))/2),
                    xi = 4*sqrt(log(n*p))
)
resX 
resY = Inspect_test(Y, 
                    lambda = sqrt(log(p*log(n))/2),
                    xi = 4*sqrt(log(n*p))
)
resY

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

# Manual empirical choice of thresholds (equivalent to the above)
thresholds_test_emp = Inspect_test_calibrate(n,p, N=100, tol=1/100)
resX = Inspect_test(X, xi = thresholds_test_emp$max_value)
resX
resY = Inspect_test(Y, xi = thresholds_test_emp$max_value)
resY