single_ESAC {HDCD}

Efficient Sparsity Adaptive Change-point estimator for a single change-point

Description

R wrapper for C function implementing ESAC for single change-point estimation, as described in section 3.1 in Moen et al. (2023)

Usage

single_ESAC(
  X,
  threshold_d = 1.5,
  threshold_s = 1,
  rescale_variance = FALSE,
  debug = FALSE
)

Arguments

X

Matrix of observations, where each row contains a time series

threshold_d

Leading constant for \lambda(t) \propto r(t) for t= p

threshold_s

Leading constant for \lambda(t) \propto r(t) for t\leq \sqrt{p\log 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

pos

estimated change-point location

s

the value of t \in \mathcal{T} at which the sparsity specific score is maximized

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 = 500
p = 500
set.seed(101)
# Generating data
X = matrix(rnorm(n*p), ncol = n, nrow=p)
# Adding a single sparse change-point:
X[1:5, 201:500] = X[1:5, 201:500] +1

res = single_ESAC(X,rescale_variance=TRUE)
res$pos

# Manually setting the leading constants for \lambda(t):
# here \lambda(t) = 2 (\sqrt{p \log(n^4)}  + \log (n^4)) for t=p
# and             = 2 (t \log (ep\log n^4 / t^2) + \log(n^4))
res = single_ESAC(X, threshold_d = 2, threshold_s = 2)
res$pos