cpt_consistent_var function

Variance Estimation Consistent Under Change

Estimate the variance (using the sum of squared errors) with an estimator that is consistent when the mean changes at a known point.

cpt_consistent_var(x, k)

Arguments

• x: A numeric vector for the data set
• k: The potential change point at which the data set is split

Returns

The estimated change-consistent variance

Details

This is the estimator

where $\bar{X}_t = t^{-1}\sum_{s = 1}^t X_s$ and c("$\\tilde{X}_{T - t} =\n$", "$(T - t)^{-1} \\sum_{s = t + 1}^{T} X_s$"). In this implementation, $T$ is computed automatically as length(x) and k corresponds to $t$, a potential change point.

Examples

CPAT:::cpt_consistent_var(c(rnorm(500, mean = 0), rnorm(500, mean = 1)), k = 500)