ESAC_test_calibrate: Generates empirical penalty function gamma(t) for single...

In HDCD: High-Dimensional Changepoint Detection

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 \insertCitemoen2023efficient;textualHDCD, 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

\insertAllCited

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

HDCD documentation built on June 22, 2024, 10:53 a.m.