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)
x |
A numeric vector for the data set |
k |
The potential change point at which the data set is split |
This is the estimator
\hat{σ}^2_{T,t} = T^{-1}≤ft(∑_{s = 1}^t ≤ft(X_s - \bar{X}_t\right)^2 + ∑_{s = t + 1}^{T}≤ft(X_s - \tilde{X}_{T - t} \right)^2\right)
where \bar{X}_t = t^{-1}∑_{s = 1}^t X_s and \tilde{X}_{T - t} =
(T - t)^{-1} ∑_{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.
The estimated change-consistent variance
CPAT:::cpt_consistent_var(c(rnorm(500, mean = 0), rnorm(500, mean = 1)), k = 500)
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