I1 Mean-Change Testing and DCI Candidate Detection

Computes the I1 statistic for mean changes and generates multiple candidate change locations using adaptive contrasts and local interquartile scaling. Provides empirical I1 p-values for independent Gaussian series of length 100 with full-window parameter 22, statistic-only analysis for other settings, and weighted and unweighted segmentation covering scores. DCI candidate detection is descriptive and does not assign significance to selected segments. Based on the methodology of Waychal, Laha and Sinha (2026) .

DCIi1

I1 mean-change testing and descriptive DCI candidate detection, based on Waychal, Laha and Sinha (2026), arXiv:2610.23476.

Installation

install.packages("DCIi1_0.2.0.tar.gz", repos = NULL, type = "source")
library(DCIi1)

I1 test

Reference p-values require 100 observations, w1=22 and independent Gaussian noise. The input checks enforce length, window and mode; the user assesses the noise assumption. Mean-shift alternatives are allowed.

set.seed(12)
y <- rnorm(100) + rep(c(0, 3), each = 50)
result <- i1_test(y)
result
attr(result, "diagnostics")

The calibration is an empirical density approximation. In 10000 independent Gaussian null validation series, rejection rates were 0.86%, 4.15% and 8.57% at nominal levels 1%, 5% and 10%. This is finite-sample evidence, not a claim of exact size or validity under other distributions.

For other lengths, windows or WD scaling, use statistic-only analysis:

set.seed(13)
long_series <- rnorm(300)
i1_test(long_series, calibration = "none")  # pvalue is NA
i1_stt(long_series)
i1_test(y, archeck = 1, calibration = "none")

DCI candidate locations

DCI flags and refines candidate mean changes. It does not assign p-values to data-selected segments or label candidates statistically significant.

set.seed(21)
y_multi <- rnorm(160) + rep(c(0, 4, -3, 1), c(50, 15, 15, 80))
candidates <- dcii1(y_multi)
locations <- change_points(candidates)
plot(y_multi, type = "l", xlab = "Observation", ylab = "Value")
abline(v = locations, col = "firebrick", lty = 2)
covering_metric_unwtd(160, c(50, 65, 80), locations)

All DCI pvalue entries are NA. Candidate locations can occur under a constant mean. change_points() sorts and deduplicates candidates without testing them. Locations are the last observation before a boundary. Magnitudes are signed standardized contrasts, not original-unit shifts. For I1, multiply cpmag by the diagnostics sigma to recover data units.

Practical scope

• Numeric finite univariate data; no implicit missing-value deletion.
• Default full window 22 means up to 11 observations on each side.
• The WD denominator is -2 * sqrt(2) * (1-rho) * qnorm(.25), as in Appendix B.1.
• Zero IQR, undefined WD estimates and unsupported inferential settings error explicitly.
• No asymptotic p-values, multiplicity adjustment, or general variance-change test.
• No external data downloads, workspace loading or compiled code are needed.

See ?i1_test, ?dcii1, vignette("i1-test", package="DCIi1") and vignette("dci-algorithm", package="DCIi1").

Authors and licence

Nachiketas Waychal, Arnab Kumar Laha and Ankur Sinha are the software authors and copyright holders. Maintainer: Nachiketas Waychal [email protected]. Distributed under GPL-3. Affiliations, attribution and AI-assisted development acknowledgement are in inst/NOTICE. Cite the method with citation("DCIi1").