Asymptotic statistical properties of communication-efficient quickest detection schemes in sensor networks. (English) Zbl 1431.62337
The authors analyze the quickest change detection problem related to monitoring a large number \(K\) of data streams in sensor networks when the “trigger” event may affect different sensors differently. The motivation of the research is censoring sensor networks. In the paper scalable communication-efficient schemes based on the sum of local cumulative sum (CUSUM) statistics are investigated. It is extended to the detection delay analysis of these communication efficient schemes in the context of monitoring \(K\) independent data streams. The asymptotic statistical properties under two regimes: one is the classical asymptotic regime when the dimension \(K\) is fixed, and the other is the modern asymptotic regime when the dimension \(K\) goes to 1 is established. The relations between communication efficiency and statistical efficiency is shown.
Sensor networks have broad applications. One of them is the quickest detection of a “trigger” event when sensor networks are deployed to monitor the changing environments over time and space [V. V. Veeravalli, IEEE Trans. Inf. Theory 47, No. 4, 1657–1665 (2001; Zbl 1017.94516)]. Shortening the wait for the right moment to decide about the detection of a “trigger” event is implemented in different ways [P. Braca et al., Signal Process. 91, No. 4, 919–930 (2011; Zbl 1217.94035)] with the running consensus scheme, [V. V. Veeravalli, J. Franklin Inst. 336, No. 2, 301–322 (1999; Zbl 1048.90125)] with some kind of linkage of sensors decision and [K. Szajowski, in: Stochastic models, statistics and their applications. Cham: Springer. 187–195 (2015; Zbl 1349.62203)] with the winning coalition in the simple game of sensors.
Sensor networks have broad applications. One of them is the quickest detection of a “trigger” event when sensor networks are deployed to monitor the changing environments over time and space [V. V. Veeravalli, IEEE Trans. Inf. Theory 47, No. 4, 1657–1665 (2001; Zbl 1017.94516)]. Shortening the wait for the right moment to decide about the detection of a “trigger” event is implemented in different ways [P. Braca et al., Signal Process. 91, No. 4, 919–930 (2011; Zbl 1217.94035)] with the running consensus scheme, [V. V. Veeravalli, J. Franklin Inst. 336, No. 2, 301–322 (1999; Zbl 1048.90125)] with some kind of linkage of sensors decision and [K. Szajowski, in: Stochastic models, statistics and their applications. Cham: Springer. 187–195 (2015; Zbl 1349.62203)] with the winning coalition in the simple game of sensors.
Reviewer: Krzysztof J. Szajowski (Wrocław)
MSC:
| 62L15 | Optimal stopping in statistics |
| 60G40 | Stopping times; optimal stopping problems; gambling theory |
| 62R07 | Statistical aspects of big data and data science |
| 62N01 | Censored data models |
| 94A13 | Detection theory in information and communication theory |
| 62G10 | Nonparametric hypothesis testing |
Keywords:
asymptotic optimality; change point; detection delay; false alarm rate; high-dimensional data; dynamical analysis of statistical dataReferences:
| [1] | Appadwedula, S.; Veeravalli, V. V.; Jones, D., Energy-Efficient Detection in Sensor Networks,, IEEE Journal on Selected Areas in Communications, 23, 693-702 (2005) |
| [2] | Banerjee, S.; Fellouris, G., Proceedings of 2016 IEEE International Symposium on Information Theory (ISIT 2016), Decentralized Sequential Change Detection with Ordered CUSUMs (2016), Barcelona, Spain |
| [3] | Banerjee, T.; Veeravalli, V. V., Data-Efficient Quickest Change Detection in Sensor Networks, IEEE Transactions on Signal Processing, 63, 3727-3735 (2015) · Zbl 1394.94067 |
| [4] | Basseville, M.; Nikiforov, I. V., Detection of Abrupt Changes: Theory and Applications, Englewood Cliffs (1993), Prentice Hall · Zbl 1407.62012 |
| [5] | Candès, E. J., Modern Statistical Estimation via Oracle Inequalities,, Acta Numerica, 15, 257-325 (2006) · Zbl 1141.62001 |
| [6] | Chan, H. P., Optimal Sequential Detection in Multi-Stream Data,, Annals of Statistics, 45, 2736-2763 (2017) · Zbl 1388.62127 |
| [7] | Donoho, D. L.; Johnstone, I. M., Ideal Spatial Adaptation by Wavelet Shrinkage,, Biometrika, 81, 425-455 (1994) · Zbl 0815.62019 |
| [8] | Fan, J.; Lin, S. K., Test of Significance When Data are Curves,, Journal of American Statistical Association, 93, 1007-1021 (1998) · Zbl 1064.62525 |
| [9] | Fuh, C. D.; Mei, Y., Quickest Change Detection and Kullback-Leibler Divergence for Two-State Hidden Markov Models, IEEE Transactions on Signal Processing, 63, 4866-4878 (2015) · Zbl 1394.94808 |
| [10] | Glaz, J.; Naus, J.; Wallenstein, S., Scan Statistics (2001), New York: Springer, New York · Zbl 0983.62075 |
| [11] | Kiefer, J.; Sacks, J., Asymptotically Optimum Sequential Inference and Design,, Annals of Mathematical Statistics, 34, 705-750 (1963) · Zbl 0255.62063 |
| [12] | Kulldorff, M., Prospective Time-Periodic Geographic Disease Surveillance Using a Scan Statistic,, Journal of Royal Statistical Society, Series A, 164, 61-72 (2001) · Zbl 1002.62517 |
| [13] | Lai, T. L., Sequential Change-Point Detection in Quality Control and Dynamical Systems (with Discussions),, Journal of Royal Statistical Society, Series B, 57, 613-658 (1995) · Zbl 0832.62072 |
| [14] | Lai, T. L., Sequential Analysis: Some Classical Problems and New Challenges, Statistica Sinica, 11, 303-408 (2001) · Zbl 1037.62081 |
| [15] | Liu, K.; Mei, Y.; Shi, J., An Adaptive Sampling Strategy for Online High-Dimensional Process Monitoring,, Technometrics, 57, 305-319 (2015) |
| [16] | Liu, K.; Zhang, R.; Mei, Y., Scalable Sum-Shrinkage Schemes for Distributed Monitoring Large-Scale Data Streams (2019), Statistica Sinica · Zbl 1412.62070 |
| [17] | Lorden, G., Procedures for Reacting to a Change in Distribution,, Annals of Mathematical Statistics, 42, 1897-1908 (1971) · Zbl 0255.62067 |
| [18] | Lorden, G.; Pollak, M., Sequential Change-Point Detection Procedures That Are Nearly Optimal and Computationally Simple,, Sequential Analysis, 27, 476-512 (2008) · Zbl 1149.62069 |
| [19] | Mei, Y., Information Bounds and Quickest Change Detection in Decentralized Decision Systems,, IEEE Transactions on Information Theory, 51, 2669-2681 (2005) · Zbl 1310.94038 |
| [20] | Mei, Y., Efficient Scalable Schemes for Monitoring a Large Number of Data Streams,, Biometrika, 97, 419-433 (2010) · Zbl 1406.62088 |
| [21] | Mei, Y., IEEE International Symposium on Information Theory (ISIT), Quickest Detection in Censoring Sensor Networks (2011) |
| [22] | Montgomery, D. C., Introduction to Statistical Quality Control (1991), New York: Wiley, New York |
| [23] | Moustakides, G. V., Optimal Stopping Times for Detecting Changes in Distributions,, Annals of Statistics, 14, 1379-1387 (1986) · Zbl 0612.62116 |
| [24] | Neyman, J., Smooth Test for Goodness-of-Fit, Scandinavian Actuarial Journal, 20, 149-199 (1937) · JFM 63.1092.02 |
| [25] | Page, E. S., Continuous Inspection Schemes, Biometrika, 41, 100-115 (1954) · Zbl 0056.38002 |
| [26] | Pollak, M., Optimal Detection of a Change in Distribution,, Annals of Statistics, 13, 206-227 (1985) · Zbl 0573.62074 |
| [27] | Pollak, M., Average Run Lengths of an Optimal Method of Detecting a Change in Distribution,, Annals of Statistics, 15, 749-779 (1987) · Zbl 0632.62080 |
| [28] | Poor, H. V.; Hadjiliadis, O., Quickest Detection (2009), New York: Cambridge University Press, New York · Zbl 1393.60039 |
| [29] | Rago, C.; Willett, P.; Bar-Shalom, Y., Censoring Sensors: A Low-Communication-Rate Scheme for Distributed Detection,, IEEE Transactions on Aerospace and Electronic Systems, 32, 554-568 (1996) |
| [30] | Roberts, S. W., A Comparison of Some Control Chart Procedures,, Technometrics, 8, 411-430 (1966) |
| [31] | Shewhart, W. A., Economic Control of Quality of Manufactured Product (1931), WI: ASQC Quality Press, WI |
| [32] | Shiryaev, A. N., On Optimum Methods in Quickest Detection Problems,, Theory of Probability & Its Applications, 8, 22-46 (1963) · Zbl 0213.43804 |
| [33] | Siegmund, D., Sequential Analysis: Tests and Confidence Intervals (1985), New York: Springer, New York · Zbl 0573.62071 |
| [34] | Tartakovsky, A. G.; Nikiforov, I.; Basseville, M., Sequential Analysis: Hypothesis Testing and Changepoint Detection (2014), Chapman and Hall/CRC |
| [35] | Tartakovsky, A. G.; Rozovskiia, B. L.; Blazeka, R. B.; Kim, H., Detection of Intrusions in Information Systems by Sequential Change-Point Methods (with Discussions),, Statistical Methodology, 3, 252-340 (2006) · Zbl 1248.94032 |
| [36] | Tartakovsky, A. G.; Veeravalli, V. V.; Mukhopadhyay, N.; Datta, S.; Chattopadhyay, S., Applications of Sequential Methodologies, Change-Point Detection in Multichannel and Distributed Systems, 339-370 (2004), New York: Dekker, New York · Zbl 1082.62068 |
| [37] | Tay, W. P.; Tsitsiklis, J. N.; Win, M. Z., Asymptotic Performance of a Censoring Sensor Network,, IEEE Transactions on Information Theory, 53, 4191-4209 (2007) · Zbl 1326.94033 |
| [38] | Veeravalli, V. V., Decentralized Quickest Change Detection,, IEEE Transactions on Information Theory, 47, 1657-1665 (2001) · Zbl 1017.94516 |
| [39] | Wang, Y.; Mei, Y., Large-Scale Multi-Stream Quickest Change Detection via Shrinkage Post-Change Estimation,, IEEE Transactions on Information Theory, 61, 6926-6938 (2015) · Zbl 1359.94227 |
| [40] | Wang, Y.; Mei, Y.; Paynabar, K., Thresholded Multivariate Principal Component Analysis for Phase I Multichannel Profile Monitoring,, Technometrics, 60, 360-372 (2018) |
| [41] | Xian, X.; Wang, A.; Liu, K., A Nonparametric Adaptive Sampling Strategy for Online Monitoring of Big Data Streams,, Technometrics, 60, 14-25 (2018) |
| [42] | Xie, Y.; Siegmund, D., Sequential Multi-Sensor Change-Point Detection,, Annals of Statistics, 41, 670-692 (2013) · Zbl 1267.62084 |
| [43] | Zhang, R.; Mei, Y.; Shi, J.; Zhao, Y.; Chen, D. G., New Frontiers in Biostatistics and Bioinformatics, Wavelet-Based Profile Monitoring Using Order-Thresholding Recursive CUSUM Schemes (2018), Switzerland: Springer, Switzerland |
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