| 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 thePCpluS estimatorF. Pein (2021). The values obtained can be used in the estimatorpcplus.
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 |
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 |
nbandwidth | a single integer giving the length of the grid for |
nlambda | a single integer giving the length of the grid for |
lambda.min.ratio | a single numeric between |
sd | a single positive value giving the standard deviation of the observations; may be |
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 |
maxit | a single positive integer giving the maximum number of passes over the data for all lambda values |
Value
alist containing the entrieslambda andbandwidth giving the best parameter for the tuning parameters. Both can be passed directly topcplus. Note thatlambda 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 entriescv with the loss for the selected parameters,bandwidths with the grid of bandwidths used, andcvs 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
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 thePCpluS estimatorF. Pein (2021) for a given bandwidth and the penalty lambda. Bandwidth and lambda can be obtained by cross-validation using the functioncv.pcplus. ThePCpluS 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 |
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 |
nlambda | a single positive integer specifying the number of lambda values to pass to the lasso; only used if |
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 |
maxit | a single positive integer giving the maximum number of passes over the data for all lambda values |
Value
alist containing the entriesest with the fitted values of the esitmator,smooth with the smooth part of the estimator,cpfun with the change-point part of the estimator, andcps 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
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)