stepR (version 2.1-10)

stepsel: Automatic selection of number of jumps

Description

Select the number of jumps.

Usage

stepsel(path, y, type = c("MRC", "AIC", "BIC"), ...)
stepsel.MRC(path, y, q, alpha = 0.05, r = ceiling(50 / min(alpha, 1 - alpha)),
  lengths = if(attr(path$cand, "family") == "gaussKern")
    2^(floor(log2(length(y))):ceiling(log2(length(attr(path$cand, "param")$kern)))) else
    2^(floor(log2(length(y))):0),
  penalty = c("none", "log", "sqrt"), name = if(attr(path$cand, "family") == "gaussKern")
    ".MRC.ktable" else ".MRC.table",
  pos = .MCstepR)
stepsel.AIC(path, ...)
stepsel.BIC(path, ...)

Value

A single integer giving the number of blocks selected, with attribute crit containing the values of the criterion (MRC / AIC / BIC) for each fit in the path.

Arguments

path

an object of class steppath

y

for type=MRC only: a numeric vector containing the serial data

type

how to select, dispatches specific method

...

further argument passed to specific method

q, alpha, r, lengths, penalty, name, pos

see bounds

References

Boysen, L., Kempe, A., Liebscher, V., Munk, A., Wittich, O. (2009) Consistencies and rates of convergence of jump-penalized least squares estimators. The Annals of Statistics 37(1), 157--183.

Yao, Y.-C. (1988) Estimating the number of change-points via Schwarz' criterion. Statistics & Probability Letters 6, 181--189.

See Also

steppath, stepfit, family, stepbound

Examples

# simulate 5 blocks (4 jumps) within a total of 100 data points
b <- c(sort(sample(1:99, 4)), 100)
f <- rep(rnorm(5, 0, 4), c(b[1], diff(b)))
rbind(b = b, f = unique(f))
# add gaussian noise
y <- f + rnorm(100)
# find 10 candidate jumps
path <- steppath(y, max.cand = 10)
# select number of jumps by simulated MRC with sqrt-penalty
# thresholded with positive delta, and by BIC
sel.MRC <- stepsel(path, y, "MRC", alpha = 0.05, r = 1e2, penalty = "sqrt")
sel.MRC
delta <- .1
sel.delta <- stepsel(path, y, "MRC",
  q = (1 + delta) * sdrobnorm(y) * sqrt(2 * length(y)), penalty = "none")
sel.delta
sel.BIC <- stepsel(path, type="BIC")
sel.BIC
# compare results with truth
fit.MRC <- path[[sel.MRC]]
as.data.frame(fit.MRC)
as.data.frame(path[[sel.delta]])
as.data.frame(path[[sel.BIC]])