×

Real-time change point detection in linear models using the ranking selection procedure. (English) Zbl 07708161

Summary: We propose a novel sequential change point detection method in linear models. Our method uses a given historical data set to determine the prechange model. Significant features are selected using the ranking procedure, which is an innovative approach aimed at revealing the rank of all features in terms of their effects on the model. We establish the asymptotic properties of the test statistic under the null and alternative hypotheses. Simulations are conducted to illustrate the performance of the proposed method. We conclude with a real data application to illustrate the detection procedure.

MSC:

62Lxx Sequential statistical methods
Full Text: DOI

References:

[1] Bechhofer, R. E., A Single-Sample Multiple Decision Procedure, Annals of Mathematical Statistics, 25, 1, 16-39 (1954) · Zbl 0055.13003
[2] Bechhofer, R. E.; Dunnett, C. W.; Sobel, M., A Two-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with a Common Unknown Variance, Biometrika, 41, 1-2, 170-6 (1954) · Zbl 0056.13002
[3] Candes, E.; Tao, T., The Dantzig Selector: Statistical Estimation When p is Much Larger than n, Annals of Statistics, 35, 6, 2313-51 (2007) · Zbl 1139.62019
[4] Chen, H., Sequential Change-Point Detection Based on Nearest Neighbors, The Annals of Statistics, 47, 3, 1381-407 (2019) · Zbl 1419.62201
[5] Chu, C.-S.; Stinchcombe, M.; White, H., Monitoring Structural Change, Econometrica, 64, 5, 1045-65 (1996) · Zbl 0856.90027
[6] Chu, L.; Chen, H., Asymptotic Distribution-Free Change-Point Detection for Multivariate and Non-Euclidean Data, The Annals of Statistics, 47, 1, 382-414 (2019) · Zbl 1417.62114
[7] Ciuperca, G., Real Time Change-Point Detection in a Model by Adaptive Lasso and Cusum, Journal de la Société Française de Statistique, 156, 4, 113-32 (2015) · Zbl 1338.62129
[8] Fan, J.; Li, R., Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties, Journal of the American Statistical Association, 96, 1348-60 (2001) · Zbl 1073.62547
[9] Gu, C., Advancing Bechhofer’s Ranking Procedures to High-Dimensional Variable Selection, 81 (2021), Bowling Green State University
[10] Horváth, L.; Huškova, M.; Kokoszká, P.; Steinebach, J., Monitoring Changes in Linear Models, Journal of Statistical Planning and Inference, 126, 225-51 (2004) · Zbl 1075.62054
[11] Horváth, L.; Kokoszka, P.; Steinebach, J., On Sequential Detection of Parameter Changes in Linear Regression, Statistics and Probability Letters, 77, 9, 885-95 (2007) · Zbl 1117.62079
[12] Lorden, G., Procedures for Reacting to a Change in Distribution, The Annals of Mathematical Statistics, 42, 6, 1897-908 (1971) · Zbl 0255.62067
[13] Page, E. S., Continue Inspection Schemes, Biometrika, 41, 100-35 (1954) · Zbl 0056.38002
[14] Ratnasingam, S.; Ning, W., Monitoring Sequential Structural Changes in Penalized High-Dimensional Linear Models, Sequential Analysis, 40, 3, 381-404 (2021) · Zbl 1479.62054
[15] Ratnasingam, S.; Ning, W., Sequential Change Point Detection for High‐Dimensional Data Using Nonconvex Penalized Quantile Regression, Biometrical Journal, 63, 3, 575-98 (2021) · Zbl 1523.62187
[16] Rhee, S.-Y.; Taylor, J.; Wadhera, G.; Ben-Hur, A.; Brutlag, D. L.; Shafer, R. W., Genotypic Predictors of Human Immunodeficiency Virus Type 1 Drug Resistance, Proceedings of the National Academy of Sciences, 103, 17355-60 (2006)
[17] Roberts, S. W., A Comparison of Some Control Chart Procedures, Technometrics, 8, 411-30 (1966)
[18] Shiryaev, A. N., On Optimum Methods in Quickest Detection Problems, Theory of Probability and Its Applications, 8, 1, 22-46 (1963) · Zbl 0213.43804
[19] Siegmund, D., Sequential Analysis: Tests and Confidence Intervals (1985), New York: Springer · Zbl 0573.62071 · doi:10.1007/978-1-4757-1862-1
[20] Tartakovsky, A.; Nikiforov, I.; Basseville, M., Sequential Analysis: Hypothesis Testing and Changepoint Detection (2014), Chapman and Hall/CRC · doi:10.1201/b17279
[21] Tibshirani, R., Regression Shrinkage and Selection via the Lasso, Journal of the Royal Statistical Society Series B, 58, 1, 267-88 (1996) · Zbl 0850.62538
[22] Yuan, M.; Lin, Y., Model Selection and Estimation in Regression with Grouped Variables, Journal of the Royal Statistical Society Series B, 68, 1, 49-67 (2006) · Zbl 1141.62030
[23] Zhang, C.-H., Nearly Unbiased Variable Selection under Minimax Concave Penalty, Annals of Statistics, 38, 2, 894-942 (2010) · Zbl 1183.62120
[24] Zhou, M.; Wang, H.; Tang, Y., Sequential Change Point Detection in Linear Quantile Regression Models, Statistics and Probability Letters, 100, 98-103 (2015) · Zbl 1396.62086
[25] Zou, H., The Adaptive Lasso and Its Oracle Properties, Journal of the American Statistical Association, 101, 476, 1418-28 (2006) · Zbl 1171.62326
[26] Zou, H.; Hastie, T., Regularization and Variable Selection via the Elastic Net, Journal of the Royal Statistical Society, 67, 2, 301-20 (2005) · Zbl 1069.62054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.