nsp: Narrowest Significance Pursuit algorithm with general...
In nsp: Inference for Multiple Change-Points in Linear Models

Description Usage Arguments Details Value Author(s) See Also Examples

This function runs the bare-bones Narrowest Significance Pursuit (NSP) algorithm on data sequence y and design matrix x to obtain localised regions (intervals) of the domain in which the parameters of the linear regression model y_t = beta(t) x_t + z_t significantly depart from constancy (e.g. by containing change-points). For any interval considered by the algorithm, significance is achieved if the multiscale supremum-type deviation measure (see Details for the literature reference) exceeds lambda. This function is mainly to be used by the higher-level functions nsp_poly, nsp_poly_ar and nsp_tvreg (which estimate a suitable lambda so that a given global significance level is guaranteed), and human users may prefer to use those functions instead; however, nsp can also be run directly, if desired. The function works best when the errors z_t in the linear regression formulation y_t = beta(t) x_t + z_t are independent and identically distributed Gaussians.

1	nsp(y, x, M, lambda, overlap = FALSE, buffer = 0)

`y`	A vector containing the data sequence being the response in the linear model y_t = beta(t) x_t + z_t.
`x`	The design matrix in the regression model above, with the regressors as columns.
`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.
`lambda`	The threshold parameter for measuring the significance of non-constancy (of the linear regression parameters), for use with the multiscale supremum-type deviation measure described in the paper.
`overlap`	If `FALSE`, then on discovering a significant interval, the search continues recursively to the left and to the right of that interval. If `TRUE`, then the search continues to the left and to the right of the midpoint of that interval.
`buffer`	A non-negative integer specifying how many observations to leave out immediately to the left and to the right of a detected interval of significance before recursively continuing the search for the next interval.

The NSP algorithm is described in P. Fryzlewicz (2021) "Narrowest Significance Pursuit: inference for multiple change-points in linear models", preprint.

A list with the following components:

`intervals`	A data frame containing the estimated intervals of significance: `starts` and `ends` is where the intervals start and end, respectively; `values` are the values of the deviation measure on each given interval; `midpoints` are the midpoints of the intervals.
`threshold.used`	The threshold `lambda`.

Piotr Fryzlewicz, p.fryzlewicz@lse.ac.uk

nsp_poly, nsp_poly_ar, nsp_tvreg, nsp_selfnorm, nsp_poly_selfnorm

set.seed(1)
f <- c(1:100, 100:1, 1:100)
y <- f + stats::rnorm(300) * 15
x <- matrix(0, 300, 2)
x[,1] <- 1
x[,2] <- seq(from = 0, to = 1, length = 300)
nsp(y, x, 100, 15 * thresh_kab(300, .1))