HDCD (version 1.0)

Inspect_test: Inspect single change-point test

Description

R wrapper for C function testing for a single change-point using Inspect wang_high_2018;textualHDCD.

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
)

Value

1 if a change-point is detected, 0 otherwise

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

References

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