L0TFinv (version 0.1.0)

TFmetrics: Print four metrics about change point detection results

Description

Prints four metrics to compare the quality of change point detection results.

Usage

TFmetrics(y0, tau = NULL, yhat, cpts = NULL)

Value

MSE

The mean square error between the fitted trend and the underlying trend

MAD

The median absolute deviation between the fitted trend and the underlying trend

dH

Hausdorff Distance (dH) measures the accuracy of the estimated change points

nknot

The number of detected change points

Arguments

y0

The underlying trend

tau

The locations of change points in the underlying trend

yhat

The fitted trend

cpts

The positions of the fitted change points

Details

\(\hat{\boldsymbol{\tau}}\) represents the estimated change point positions, while \(\boldsymbol{\tau}\) denotes the locations of change points in the underlying trend. $$d_H=\frac{1}{n} \max \{\max_k \min_j |\tau_j-\hat{\tau}_k|,\max_j \min_k |\tau_j-\hat{\tau}_k|\}.$$ Note that the number of \(\hat{\boldsymbol{\tau}}\) and \(\boldsymbol{\tau}\) does not need to be the same.

Examples

tau = c(0.1, 0.3, 0.4, 0.7, 0.85)
h = c(-1, 5, 3, 0, -1, 2)
n = 500
BlocksData <- SimuBlocksInv(n = n, sigma = 0.2, seed = 50, tau = tau ,h = h)
res <- L0TFinv.opt(y=BlocksData$y, kmax=10, q=0, first=0.01, last=1, penalty="bic")
metrics <- TFmetrics(BlocksData$y0,BlocksData$tau,res$yopt,res$Aopt/n)
print(metrics)

tau1 = c(0.1, 0.3, 0.4, 0.7, 0.85)
h1 = c(-1, 5, 3, 0, -1, 2)
a0 = -10
n1 = 2000
WaveData <- SimuWaveInv(n = n1, sigma = 0.1, seed = 50, tau = tau1, h = h1, a0 = a0)
res1 <- L0TFinv.fix(y=WaveData$y, k=20, q=1, first=0, last=0.99)
metrics1 <- TFmetrics(WaveData$y0,WaveData$tau,res1$y.all[,5],res1$A.all[[5]]/n1)
print(metrics1)