CUSUM: CUSUM transformation of a matrix

In HDCD: High-Dimensional Changepoint Detection

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 \insertCiteinspectpackageHDCD.

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

\insertAllCited

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)

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