cpt_consistent_var {CPAT}

Variance Estimation Consistent Under Change

Description

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

Usage

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

Details

This is the estimator

\hat{\sigma}^2_{T,t} = T^{-1}\left(\sum_{s = 1}^t \left(X_s - \bar{X}_t\right)^2 + \sum_{s = t + 1}^{T}\left(X_s - \tilde{X}_{T - t} \right)^2\right)

where \bar{X}_t = t^{-1}\sum_{s = 1}^t X_s and \tilde{X}_{T - t} = (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.

Value

The estimated change-consistent variance

Examples

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