nsp_poly_selfnorm {nsp} | R Documentation |
Self-normalised Narrowest Significance Pursuit algorithm for piecewise-polynomial signals
Description
This function runs the Narrowest Significance Pursuit (NSP) algorithm on a data sequence y
believed to follow the model
y_t = f_t + z_t, where f_t is a piecewise polynomial of degree deg
, and z_t is noise. It returns localised regions (intervals) of the
domain, such that each interval must contain a change-point in the parameters of the polynomial f_t
at the global significance level alpha
.
For any interval considered by the algorithm,
significant departure from parameter constancy is achieved if the multiscale
deviation measure (see Details for the literature reference) exceeds a threshold, which is either provided as input
or determined from the data (as a function of alpha
). The function assumes independence, symmetry and finite variance of the
errors z_t, but little else; in particular they do not need to have a constant variance across t.
Usage
nsp_poly_selfnorm(
y,
M = 1000,
thresh.val = NULL,
power = 1/2,
min.size = 20,
alpha = 0.1,
deg = 0,
eps = 0.03,
c = exp(1 + 2 * eps),
overlap = FALSE
)
Arguments
y |
A vector containing the data sequence. |
M |
The minimum number of intervals considered at each recursive stage, unless the number of all intervals is smaller, in which case all intervals are used. |
thresh.val |
Numerical value of the significance threshold (lambda in the paper); or |
power |
A parameter for the (rough) estimator of the global sum of squares of z_t; the span of the moving window in that estimator is
|
min.size |
(See immediately above.) |
alpha |
Desired maximum probability of obtaining an interval that does not contain a change-point (the significance threshold will be determined as a function of this parameter). |
deg |
The degree of the polynomial pieces in f_t (0 for the piecewise-constant model; 1 for piecewise-linearity, etc.). |
eps |
Parameter of the self-normalisation statistic as described in the paper; use default if unsure how to set. |
c |
Parameter of the self-normalisation statistic as described in the paper; use default if unsure how to set. |
overlap |
If |
Details
The NSP algorithm is described in P. Fryzlewicz (2021) "Narrowest Significance Pursuit: inference for multiple change-points in linear models", preprint.
Value
A list with the following components:
intervals |
A data frame containing the estimated intervals of significance: |
threshold.used |
The threshold value. |
Author(s)
Piotr Fryzlewicz, p.fryzlewicz@lse.ac.uk
See Also
nsp_poly
, nsp_poly
, nsp_poly_ar
, nsp_tvreg
, nsp_selfnorm
Examples
set.seed(1)
g <- c(rep(0, 100), rep(10, 100), rep(0, 100))
x.g <- g + stats::rnorm(300) * seq(from = 1, to = 4, length = 300)
nsp_poly_selfnorm(x.g, 100)