Title: Piecewise Constant Plus Smooth Regression
Version: 1.0.1
Depends: R (≥ 3.0.2)
Imports: Rcpp (≥ 0.12.3), changepoint, methods, Matrix
LinkingTo: Rcpp (≥ 0.12.3), RcppEigen
Suggests: testthat (≥ 1.0.0), glmnet
Description: Allows for nonparametric regression where one assumes that the signal is given by the sum of a piecewise constant function and a smooth function. More precisely, it implements the estimator PCpluS (piecewise constant plus smooth regression estimator) from Pein and Shah (2025) <doi:10.48550/arXiv.2112.03878>.
License: GPL-3
NeedsCompilation: yes
Packaged: 2025-03-10 12:11:53 UTC; pein
Author: Pein Florian [aut, cre]
Maintainer: Pein Florian <f.pein@lancaster.ac.uk>
Repository: CRAN
Date/Publication: 2025-03-11 16:40:06 UTC

Tuning parameter selection by crossvalidation

Description

Selects the tuning parameters, bandwidth and the penalty lambda, of the PCpluS estimator F. Pein (2021). The values obtained can be used in the estimator pcplus.

Usage

cv.pcplus(y, bandwidth, lambda, nbandwidth = 30L, nlambda = 30L,
          lambda.min.ratio = 0.01, sd = NULL, thresh = 1e-7, maxit = 1e5L)

Arguments

y

a numeric vector containing the observations, only finite values are allowed

bandwidth

a numeric vector specifying possible values for the bandwidth of the kernel smoother; each entry must be between 2 / length(n) and 0.25 or Inf, smaller values are replaced by 2 / n and larger by Inf with a warning; see F. Pein (2021) for an interpretation of bandwidth == Inf. If missing an exponential grid of length nbandwidth will be used

lambda

a decreasing sequence of numerics specifying possible values for the penalty penalty of the fused lasso; each value must be positive. If missing an exponential grid of length nlambda is used

nbandwidth

a single integer giving the length of the grid for bandwidth; ignored if bandwidth is given

nlambda

a single integer giving the length of the grid for lambda; ignored if lambda is given

lambda.min.ratio

a single numeric between 0 and 1 speciyfing the range of the grid for lambda; ignored if lambda is given. More precisely, for each bandwdith value the largest value of the grid is chosen such that no changes are found and the smallest value is the largest value times lambda.min.ratio

sd

a single positive value giving the standard deviation of the observations; may be NULL, in which case a robust estimator is used

thresh

a single positive numeric value giving a convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the maximum change in the objective after any coefficient update is less than thresh times the null deviance

maxit

a single positive integer giving the maximum number of passes over the data for all lambda values

Value

a list containing the entries lambda and bandwidth giving the best parameter for the tuning parameters. Both can be passed directly to pcplus. Note that lambda is a decaying sequence instead of a single value. This improves the runtime of the estimator. The last value is the suggested tuning parameter. Furthermoore, it has the entries cv with the loss for the selected parameters, bandwidths with the grid of bandwidths used, and cvs with the loss for all bandwidths.

References

Pein, F. (2021). Change-point regression with a smooth additive disturbance. arXiv preprint arXiv:2112.03878.

See Also

pcplus

Examples

library(PCpluS)
set.seed(1)
y <- c(rnorm(125), rnorm(125, 3)) + sin(2 * pi * 1:250 / 250)

CV <- cv.pcplus(y)
ret <- pcplus(y, lambda = CV$lambda, bandwidth = CV$bandwidth)

plot(y, pch = 16)
lines(ret$est, col = "red")
abline(v = ret$cps)

Piecewise constant plus smooth estimation

Description

Computes the PCpluS estimator F. Pein (2021) for a given bandwidth and the penalty lambda. Bandwidth and lambda can be obtained by cross-validation using the function cv.pcplus. The PCpluS estimator returns a piecewise constant function plus a smooth function as well as the change-points of the piecewise constant function.

Usage

pcplus(y, bandwidth, lambda, sd = NULL, nlambda = 30L, thresh = 1e-7, maxit = 1e5L)

Arguments

y

a numeric vector containing the observations, only finite values are allowed

bandwidth

a single positive value specifying the bandwidth for the kernel smoother; must be between 1 / length(n) and 0.25 or Inf, smaller values are replaced by 1 / n and larger by Inf with a warning; see F. Pein (2021) for an interpretation of bandwidth == Inf

lambda

a single positive numeric or a decreasing sequence of positive numeric values giving the penalty for the fused lasso. If a sequence is passed, then only the smallest value is used to compute the estimator. However, passing a sequence of lambda values is often much faster than passing a single value

sd

a single positive value giving the standard deviation of the observations; may be NULL, in which case a robust estimator is used

nlambda

a single positive integer specifying the number of lambda values to pass to the lasso; only used if lambda is a single value, in which case an exponentially decreasing sequence is generated, with lambda being the smallest value. As explained for lambda, only this value is used for the estimator, but adding other values may reduce the run time

thresh

a single positive numeric value giving a convergence threshold for coordinate descent. Each inner coordinate-descent loop continues until the maximum change in the objective after any coefficient update is less than thresh times the null deviance

maxit

a single positive integer giving the maximum number of passes over the data for all lambda values

Value

a list containing the entries est with the fitted values of the esitmator, smooth with the smooth part of the estimator, cpfun with the change-point part of the estimator, and cps with the estimated change-point locations.

References

Pein, F. (2021). Change-point regression with a smooth additive disturbance. arXiv preprint arXiv:2112.03878.

See Also

cv.pcplus

Examples

library(PCpluS)
set.seed(1)
y <- c(rnorm(125), rnorm(125, 3)) + sin(2 * pi * 1:250 / 250)

CV <- cv.pcplus(y)
ret <- pcplus(y, lambda = CV$lambda, bandwidth = CV$bandwidth)

plot(y, pch = 16)
lines(ret$est, col = "red")
abline(v = ret$cps)