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.
cv.pcplus(y, bandwidth, lambda, nbandwidth = 30L, nlambda = 30L,
lambda.min.ratio = 0.01, sd = NULL, thresh = 1e-7, maxit = 1e5L)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.
a numeric vector containing the observations, only finite values are allowed
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
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
a single integer giving the length of the grid for bandwidth; ignored if bandwidth is given
a single integer giving the length of the grid for lambda; ignored if lambda is given
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
a single positive value giving the standard deviation of the observations; may be NULL, in which case a robust estimator is used
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
a single positive integer giving the maximum number of passes over the data for all lambda values
Pein, F. (2021). Change-point regression with a smooth additive disturbance. arXiv preprint arXiv:2112.03878.
pcplus
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)
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