On Random Distortion Testing Based Sequential Non-Parametric Hypothesis Testing

IEEE Trans. Signal Process.

Pastor

Sharma

et al. 2019

Self Cite

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.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

IEEE Trans. Signal Process.

Pastor

Sharma

et al. 2019

Self Cite

“…The theoretical analysis, the control over the error probabilities and the notion of buffer were not present in the past works [20]. A preliminary version without any analysis was presented in [1] and a truncated version of SeqRDT, T-SeqRDT, has been developed in [21], [22], where the sequential test is forced to stop if a decision is not made until a certain time. Beyond biomedical signal processing applications [20], the proposed theoretical framework can be of interest in many real world applications, including communications, radar, fault-detection and structural health monitoring.…”

Section: Introductionmentioning

confidence: 99%

Sequential Random Distortion Testing of Non-Stationary Processes

IEEE Trans. Signal Process.

Pastor

Sharma

et al. 2019

Self Cite

In this work, we propose a non-parametric sequential hypothesis test based on random distortion testing (RDT). RDT addresses the problem of testing whether or not a random signal, Ξ, observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, τ , from a fixed model, ξ0. The test is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. The need to control the probabilities of false alarm (PFA) and missed detection (PMD), while reducing the number of samples required to make a decision, leads to a novel sequential algorithm, SeqRDT. We show that under mild assumptions on the signal, SeqRDT follows the properties desired by a sequential test. We introduce the concept of a buffer and derive bounds on PFA and PMD, from which we choose the buffer size. Simulations show that SeqRDT leads to faster decisionmaking on an average compared to its fixed-sample-size (FSS) counterpart, BlockRDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).

Distributed Sequential Hypothesis Testing with Dependent Sensor Observations

Zhang

2019 53rd Asilomar Conference on Signals, Systems, and Computers

Varshney

2019

Self Cite

In this paper, we consider the problem of distributed sequential detection using wireless sensor networks (WSNs) in the presence of imperfect communication channels between the sensors and the fusion center (FC). We assume that sensor observations are spatially dependent. We propose a copulabased distributed sequential detection scheme that characterizes the spatial dependence. Specifically, each local sensor collects observations regarding the phenomenon of interest and forwards the information obtained to the FC over noisy channels. The FC fuses the received messages using a copula-based sequential test. Moreover, we show the asymptotic optimality of the proposed copula-based sequential test. Numerical experiments are conducted to demonstrate the effectiveness of our approach.