single_CUSUM: CUSUM transformation of matrix at a specific position

In HDCD: High-Dimensional Changepoint Detection

CUSUM transformation of matrix at a specific position

Description

R wrapper for C function computing the CUSUM transformation of matrix over an interval (s,e] evaluated at a specific position. For compatibility with C indexing, the user should subtract 1 from s, e and v 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].

Usage

single_CUSUM(X, start = NULL, stop = NULL, pos)

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
pos	Position at which the CUSUM should be evaluated, subtracted by one

Value

A vector of CUSUM values, each corresponding to a row of the input matrix. The i-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{pos}, 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{pos}+1.

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] evaluated at position v=4
position = 4
X_cusum_single = single_CUSUM(X,pos = position-1)
X_cusum_single

# verifying that this corresponds to the 4-th row of output of CUSUM():
X_cusum = CUSUM(X)
X_cusum[,4]

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