Retrospective Change Point Detection: From Parametric to Distribution Free Policies

• Published in: Communications in statistics. Simulation and computation Vol. 39; no. 5; pp. 899 - 920
• Main Authors: Gurevich, Gregory, Vexler, Albert
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 01.05.2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Change point; Computation; Computer simulation; CUSUM; Distribution theory; Entropy; Exact sciences and technology; Likelihood ratio; Mathematics; Most powerful; Nonparametric inference; Nonparametric likelihood; Nonparametric tests; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Optimal testing; Parametric inference; Policies; Probability and statistics; Probability theory and stochastic processes; Robustness; Sciences and techniques of general use; Shiryayev-Roberts; Statistics; Studies; Nonparametric likelihood; Statistical distribution; Generalized function; Estimator robustness; Nonparametric tests; Non parametric estimation; Entropy; Change point; Multivariate analysis; Stochastic method; Shiryayev-Roberts; Hypothesis test; Statistical test; CUSUM method; Distribution function; Most powerful; 62G20; Approximation theory; Robustness; 62F03; 62H15; Monte Carlo method; CUSUM; Non parametric test; Likelihood ratio; Statistical estimation; Statistical method; Numerical analysis; Quality control; Numerical simulation; 62G10; Optimal testing; 62G35; Parametric test
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610911003663881

The literature displays change point detection problems in the context of one of the key issues that belong to testing statistical hypotheses. The main focus in this article is to review recent retrospective change point policies and propose new relevant procedures. Commonly, applied quality control purposes have declared statements of the change point problems. Various biostatistical and engineering applications cause consideration of an extended form of the change point problem. In this article, we consider parametric and distribution free generalized change point detection policies, attending to different contexts of optimality and robustness of the procedures. We conducted a broad Monte Carlo study to compare various parametric and nonparametric tests, also investigating a sensitivity of the change point detection policies with respect to assumptions required for correct executions of the procedures. An example based on real biomarker measurements is provided to judge our conclusions.