smuceR: Piecewise constant regression with SMUCE

Description

Computes the SMUCE estimator for one-dimensional data.

Deprecation warning: This function is deprecated, but still working, however, may be defunct in a future version. Please use instead the function stepFit. At the moment some families are supported by this function that are not supported by the current version of stepFit. They will be added in a future version. An example how to reproduce results is given below.

Usage

smuceR(y, x = 1:length(y), x0 = 2 * x[1] - x[2], q = thresh.smuceR(length(y)), alpha, r,
  lengths, family = c("gauss", "gaussvar", "poisson", "binomial"), param,
  jumpint = confband, confband = FALSE)
thresh.smuceR(v)

Value

For smuceR, an object of class stepfit that contains the fit; if jumpint == TRUE function jumpint allows to extract the 1 - alpha confidence interval for the jumps, if confband == TRUE function confband allows to extract the 1 - alpha confidence band.

For thresh.smuceR, a precomputed threshhold value, see reference.

Arguments

y: a numeric vector containing the serial data
x: a numeric vector of the same length as y containing the corresponding sample points
x0: a single numeric giving the last unobserved sample point directly before sampling started
q: threshold value, by default chosen automatically according to Frick et al.~(2013)
alpha: significance level; if set to a value in (0,1), q is chosen as the corresponding quantile of the asymptotic (if r is not given) null distribution (and any value specified for q is silently ignored)
r: numer of simulations; if specified along alpha, q is chosen as the corresponding quantile of the simulated null distribution
lengths: length of intervals considered; by default up to a sample size of 1000 all lengths, otherwise only dyadic lengths
family, param: specifies distribution of data, see family
jumpint: logical (FALSE by default), indicates if confidence sets for change-points should be computed
confband: logical, indicates if a confidence band for the piecewise-continuous function should be computed
v: number of data points

References

Frick, K., Munk, A., and Sieling, H. (2014) Multiscale change-point inference. With discussion and rejoinder by the authors. Journal of the Royal Statistical Society, Series B 76(3), 495--580.

Futschik, A., Hotz, T., Munk, A. Sieling, H. (2014) Multiresolution DNA partitioning: statistical evidence for segments. Bioinformatics, 30(16), 2255--2262.

Examples

Run this code

y <- rnorm(100, c(rep(0, 50), rep(1, 50)), 0.5)

# fitted function, confidence intervals, and confidence band by stepFit
all.equal(fitted(smuceR(y, q = 1)), fitted(stepFit(y, q = 1)))
all.equal(fitted(smuceR(y, alpha = 0.5)),
          fitted(stepFit(y, q = as.numeric(quantile(stepR::MRC.1000, 0.5)))))
all.equal(fitted(smuceR(y)), fitted(stepFit(y, q = thresh.smuceR(length(y)))))

all.equal(jumpint(smuceR(y, q = 1, jumpint = TRUE)),
          jumpint(stepFit(y, q = 1, jumpint = TRUE)))
all.equal(confband(smuceR(y, q = 1, confband = TRUE)),
          confband(stepFit(y, q = 1, confband = TRUE)),
          check.attributes = FALSE)
          

# simulate poisson data with two levels
y <- rpois(100, c(rep(1, 50), rep(4, 50)))
# compute fit, q is chosen automatically
fit <- smuceR(y, family="poisson", confband = TRUE)
# plot result
plot(y)
lines(fit)
# plot confidence intervals for jumps on axis
points(jumpint(fit), col="blue")
# confidence band
lines(confband(fit), lty=2, col="blue")

# simulate binomial data with two levels
y <- rbinom(200,3,rep(c(0.1,0.7),c(110,90)))
# compute fit, q is the 0.9-quantile of the (asymptotic) null distribution
fit <- smuceR(y, alpha=0.1, family="binomial", param=3, confband = TRUE)
# plot result
plot(y)
lines(fit)
# plot confidence intervals for jumps on axis
points(jumpint(fit), col="blue")
# confidence band
lines(confband(fit), lty=2, col="blue")