stepsel {stepR}

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, ...)

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

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.

Note

To obtain the threshold described in Boysen et al.~(2009, Theorem~5), set q=(1+delta) * sdrobnorm(y) * sqrt(2*length(y)) for some positive delta and penalty="none".

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]])