# BinSegBstrap-package: Piecewise smooth regression by bootstrapped binary... In BinSegBstrap: Piecewise Smooth Regression by Bootstrapped Binary Segmentation

## Description

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).

## Acknowledgement

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'.

## References

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") ```