CUSUM {HDCD}

CUSUM transformation of a matrix

Description

R wrapper for C function computing the CUSUM transformation of a matrix over an interval (s,e]. For compatibility with C indexing, the user should subtract 1 from both s and e when supplying the arguments to the function. If start and stop are not supplied, the CUSUM is computed over the full data, so (s,e] = (0,n]. In this case, CUSUM returns the same result as cusum.transform in the package InspectChangepoint (Wang and Samworth 2020).

Usage

CUSUM(X, start = NULL, stop = NULL)

Arguments

X

Matrix of observations, where each row contains a time series

start

Starting point of interval over which the CUSUM should be computed, subtracted by one

stop

Ending point of interval over which the CUSUM should be computed, subtracted by one

Value

A matrix of CUSUM values. The (i,j)-th element corresponds to the CUSUM transformation of the i-th row of X, computed over the interval (\code{start}+1,\code{end}+1] and evaluated at position \code{start}+1+j, i.e. \sqrt{\frac{e-v}{(e-s)(v-s)}}\sum_{t=s+1}^v X_{i,t} - \sqrt{\frac{v-s}{(e-s)(e-v)}}\sum_{t=v+1}^e X_{i,t}, where s = (\code{start}+1), e = (\code{stop}+1) and v = \code{start}+1+j.

References

Wang T, Samworth R (2020). InspectChangepoint: High-Dimensional Changepoint Estimation via Sparse Projection. R package version 1.1, https://CRAN.R-project.org/package=InspectChangepoint.

Examples

n = 10
p = 10
set.seed(101)
X = matrix(rnorm(n*p), ncol = n, nrow=p)
# CUSUM over the full data (s,e] = (0,n]
X_cusum = CUSUM(X)

# CUSUM over (s,e] = (3,9]:
s = 3
e = 9
X_cusum = CUSUM(X, start = s-1, stop = e-1)