pcplus: 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)

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.

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

References

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

Examples

Run this code

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)