# cpt_consistent_var: Variance Estimation Consistent Under Change In CPAT: Change Point Analysis Tests

## 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

 1 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{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.

## Value

The estimated change-consistent variance

## Examples

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

CPAT documentation built on May 1, 2019, 6:51 p.m.