Structural change detection in ordinal time series.

Fuxiao Li,Lijuan Yang,Mengli Hao,Christophe Letellier

doi:10.1371/journal.pone.0256128

Fuxiao Li, Lijuan Yang + Show 2 more

Open Access

https://doi.org/10.1371/journal.pone.0256128

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Journal: PloS one	Publication Date: Aug 16, 2021
Citations: 2	License type: CC BY 4.0

Affiliation: Xi'an University of Technology, Chang'an University

Abstract

Change-point detection in health care data has recently obtained considerable attention due to the increased availability of complex data in real-time. In many applications, the observed data is an ordinal time series. Two kinds of test statistics are proposed to detect the structural change of cumulative logistic regression model, which is often used in applications for the analysis of ordinal time series. One is the standardized efficient score vector, the other one is the quadratic form of the efficient score vector with a weight function. Under the null hypothesis, we derive the asymptotic distribution of the two test statistics, and prove the consistency under the alternative hypothesis. We also study the consistency of the change-point estimator, and a binary segmentation procedure is suggested for estimating the locations of possible multiple change-points. Simulation results show that the former statistic performs better when the change-point occurs at the centre of the data, but the latter is preferable when the change-point occurs at the beginning or end of the data. Furthermore, the former statistic could find the reason for rejecting the null hypothesis. Finally, we apply the two test statistics to a group of sleep data, the results show that there exists a structural change in the data.

Highlights

In categorical data analysis, ordinal categorical variables are frequently encountered in many contexts, such as health status, blood pressure
There exists a structural change in the model, we will prove the consistency of the two statistics
Two test statistics based on the efficient score vector are proposed to detect the structural change of cumulative logistic regression model

Summary

Introduction

Ordinal categorical variables are frequently encountered in many contexts, such as health status (very good, good, so-so, bad, very bad), blood pressure (low, normal, high). We estimate the parameter vector θ by the partial likelihood method Consistency and asymptotic normality of the maximum partial likelihood estimator, we give a few assumptions on the the covariate matrices {Zt} and parameter vector θ. The limiting Brownian bridge is tied down at t = 0 and t = 1 (meaning B(0) = B(1) = 0), and hampers the ability of the test to detect the structural change occurring near the beginning or end of the data Many authors address this problem by adding a weight function [28].

U t ðθ 0 ÞðY ptðθ 0ÞÞÞðiÞðZtÀ 1Utðθ 0ÞðY À pt ðθ 0 ÞÞÞðjÞ

Concluding remark