Generalized Sequential Probability Ratio Test for Separate Families of Hypotheses

Li, Xiaoou; Liu, Jingchen; Ying, Zhiliang

doi:10.1080/07474946.2014.961861

Cited by 30 publications

(24 citation statements)

References 24 publications

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“…If the random walk riches the lower bound, it terminates the process and accepts the null hypothesis. Otherwise, if the random walk riches the upper bound, it terminates the process and accepts the alternate hypothesis [20].…”

Section: Methodsmentioning

confidence: 99%

Detection of black hole attack in wireless sensor network using UAV

Motamedi

Yazdani

2015

2015 7th Conference on Information and Knowledge Technology (IKT)

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The research demonstrates simulation of black hole attack in wireless sensor networks in NS2. A node is suspected to be malicious in case there is a large drop of packets by the node and as a result very few or none of the packets are allowed to reach the destination. In the first case a modified AODV protocol is presented for wireless network. The modification allows the creation of black hole node in the network and advanced dynamic routing in the simulating environment. Thereafter detecting the same by making use of random forest confusion table and contingency table generated by the classification model trace file created during simulation.

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Section: Methodsmentioning

confidence: 99%

Detection of black hole attack in wireless sensor network using UAV

Motamedi

Yazdani

2015

2015 7th Conference on Information and Knowledge Technology (IKT)

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“…where: (a) follows from Lemma A.1, (b) from the monotonicity of the Marcum function, (14) and the fact that under H 0 : 0 | Ξ N − ξ 0 | τ , and (c) from (4). The upper bounds on P FA (D N0 ) follow by substituting (22), (23) and (24) into (21) and using that a 1 ∧ a 2 a 1 . The upper bounds for P MD (D N0 ) result from a similar procedure and the definition of W * via (15).…”

Section: A False Alarm and Missed Detection Probabilitiesmentioning

confidence: 99%

“…On the other hand, WSPRT assigns a suitable weight function to the unknown parameters [16], although it is not always possible to upper bound the probabilities of error and find an appropriate weight function, even in asymptotic regimes. In contrast, GSPRT approximates the likelihood ratio by replacing the unknown parameters in the likelihood by their maximum likelihood (ML) estimates [16], [21], [22]. Various versions of GSPRT have been proposed in the literature with different thresholds [23]- [25] and most of the literature is focused on the design of one-sided tests for testing single parameter families of distributions.…”

Section: Introductionmentioning

confidence: 99%

Truncated Sequential Non-Parametric Hypothesis Testing Based on Random Distortion Testing

Khanduri

Pastor

Sharma

et al. 2019

IEEE Trans. Signal Process.

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In this work, we propose a new algorithm for sequential non-parametric hypothesis testing based on Random Distortion Testing (RDT). The data based approach is nonparametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. Our previously proposed non-truncated sequential algorithm, SeqRDT, was shown to achieve desired error probabilities under a few assumptions on the signal model. In this work, we show that the proposed truncated sequential algorithm, T-SeqRDT, requires even fewer assumptions on the signal model, while guaranteeing the error probabilities to be below pre-specified levels and at the same time makes a decision faster compared to its optimal fixedsample-size (FSS) counterpart, BlockRDT. We derive bounds on the error probabilities and the average stopping times of the algorithm. Via numerical simulations, we compare the performance of T-SeqRDT to SeqRDT, BlockRDT, sequential probability ratio test (SPRT) and composite sequential probability ratio tests. We also show the robustness of the proposed approach compared to standard likelihood ratio based approaches.

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“…The main challenge for analysis lies in characterizing the performance of the generalized sequential probability ratio test for generic families of distributions, which has not been fully understood. To that end, the recent work [28] provides the analytic tool that is instrumental to the analysis of the decentralized sequential composite test based on level-triggered sampling in this paper. Note that, in essence, [28] studied the singlesensor sequential composite test, whereas we consider the sequential composite test under the decentralized multi-sensor setup in this paper.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Sequential Composite Hypothesis Test Based on One-Bit Communication

Wang

et al. 2017

IEEE Trans. Inform. Theory

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This paper considers the sequential composite hypothesis test with multiple sensors. The sensors observe random samples in parallel and communicate with a fusion center, who makes the global decision based on the sensor inputs. On one hand, in the centralized scenario, where local samples are precisely transmitted to the fusion center, the generalized sequential likelihood ratio test (GSPRT) is shown to be asymptotically optimal in terms of the expected stopping time as error rates tend to zero.On the other hand, for systems with limited power and bandwidth resources, decentralized solutions that only send a summary of local samples (we particularly focus on a one-bit communication protocol) to the fusion center is of great importance. To this end, we first consider a decentralized scheme where sensors send their one-bit quantized statistics every fixed period of time to the fusion center. We show that such a uniform sampling and quantization scheme is strictly suboptimal and its suboptimality can be quantified by the KL divergence of the distributions of the quantized statistics under both hypotheses.We then propose a decentralized GSPRT based on level-triggered sampling. That is, each sensor runs its own GSPRT repeatedly and reports its local decision to the fusion center asynchronously. We show that this scheme is asymptotically optimal as the local thresholds and global thresholds grow large at different rates. Lastly, two particular models and their associated applications are studied to compare the centralized and decentralized approaches. Numerical results are provided to demonstrate that the proposed level-triggered sampling based decentralized scheme aligns closely with the centralized scheme with substantially lower communication overhead, and significantly outperforms the uniform sampling and quantization based decentralized scheme.

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Generalized Sequential Probability Ratio Test for Separate Families of Hypotheses

Cited by 30 publications

References 24 publications

Detection of black hole attack in wireless sensor network using UAV

Detection of black hole attack in wireless sensor network using UAV

Truncated Sequential Non-Parametric Hypothesis Testing Based on Random Distortion Testing

Decentralized Sequential Composite Hypothesis Test Based on One-Bit Communication

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