Description Acknowledgement References See Also Examples

Provides methods for piecewise smooth regression. The main function `BinSegBstrap`

estimates a piecewise smooth signal by applying a bootstrapped test recursively (binary segmentation approach). A single bootstrapped test for the hypothesis that the underlying signal is smooth versus the alternative that the underlying signal contains at least one change-point can be performed by the function `BstrapTest`

. A single change-point is estimated by the function `estimateSingleCp`

. More details can be found in the vignette. Parts of this work were inspired by Gijbels and Goderniaux (2004).

This work results from a summer research project at the University of Cambridge in 2019. Kate McDaid was supported by a bursary from the summer research programme of the Centre of Mathematics at the University of Cambridge. Florian Pein's position is funded by the EPSRC programme grant 'StatScale: Statistical Scalability for Streaming Data'.

Gijbels, I., Goderniaux, A-C. (2004) Bootstrap test for change-points in nonparametric regression. *Journal of Nonparametric Statistics* **16**(3-4), 591–611.

`BinSegBstrap`

, `BstrapTest`

, `estimateSingleCp`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
n <- 200
signal <- sin(2 * pi * 1:n / n)
signal[51:100] <- signal[51:100] + 5
signal[151:200] <- signal[151:200] + 5
y <- rnorm(n) + signal
est <- BinSegBstrap(y = y)
plot(y)
lines(signal)
lines(est$est, col = "red")
n <- 100
signal <- sin(2 * pi * 1:n / n)
signal[51:100] <- signal[51:100] + 5
y <- rnorm(n) + signal
test <- BstrapTest(y = y)
est <- estimateSingleCp(y = y)
plot(y)
lines(signal)
lines(est$est, col = "red")
``` |

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