ESAC_test_calibrate {HDCD}

Generates empirical penalty function \gamma(t) for single change-point testing using Monte Carlo simulation

Description

R wrapper for C function choosing the penalty function \gamma(t) by Monte Carlo simulation, as described in Appendix B in Moen et al. (2023), for testing for a single change-point.

Usage

ESAC_test_calibrate(
  n,
  p,
  bonferroni = TRUE,
  N = 1000,
  tol = 1/1000,
  fast = FALSE,
  rescale_variance = TRUE,
  debug = FALSE
)

Arguments

n

Number of observations

p

Number time series

bonferroni

If TRUE, a Bonferroni correction applied and the empirical penalty function \gamma(t) is chosen by simulating leading constants of r(t) through Monte Carlo simulation.

N

Number of Monte Carlo samples used

tol

False positive probability tolerance

fast

If TRUE, ESAC only tests for a change-point at the midpoint of the interval (0,\ldots,n]

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

A list containing a vector of values of \gamma(t) for t \in \mathcal{T} decreasing (element #1), a vector of corresponding values of the threshold a(t) (element # 3), a vector of corresponding values of \nu_{a(t)}

A list containing

without_partial

a vector of values of \gamma(t) for t \in \mathcal{T} decreasing in t

with_partial

same as without_partial

as

vector of threshold values a(t) for t \in \mathcal{T} decreasing in t

nu_as

vector of conditional expectations \nu_{a(t)} of a thresholded Gaussian, for t \in \mathcal{T} decreasing in t

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.

Examples

library(HDCD)
n = 50
p = 50

set.seed(100)
thresholds_emp = ESAC_test_calibrate(n,p, bonferroni=TRUE,N=100, tol=1/100)
set.seed(100)
thresholds_emp_without_bonferroni = ESAC_test_calibrate(n,p, bonferroni=FALSE,N=100, tol=1/100)
thresholds_emp[[1]] # vector of \gamma(t) for t = p,...,1
thresholds_emp_without_bonferroni[[1]] # vector of \gamma(t) for t = p,...,1

# 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] +2
resX = ESAC_test(X, thresholds = thresholds_emp[[1]])
resX
resY = ESAC_test(Y,  thresholds = thresholds_emp[[1]])
resY