Minimax optimal sequential hypothesis tests for Markov processes

@article{Fauss2018MinimaxOS,
  title={Minimax optimal sequential hypothesis tests for Markov processes},
  author={Michael Fauss and Abdelhak M. Zoubir and H. Vincent Poor},
  journal={arXiv: Statistics Theory},
  year={2018}
}
Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses is revisited and it is shown that the partial derivatives of the corresponding cost function are closely related to the performance metrics of the underlying sequential test. Second, an implicit characterization of the least favorable distributions for a… Expand

Figures and Tables from this paper

Minimax Optimal Sequential Tests for Multiple Hypotheses
  • Michael Fauss, A. Zoubir, H. Poor
  • Mathematics, Computer Science
  • 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
  • 2018
TLDR
It is shown that, in analogy to the fixed sample size case, the minimax solution is an optimal test for the least favorable distributions, i.e., a test that optimally separates the most similar feasible distributions. Expand
Bayesian Sequential Joint Detection and Estimation under Multiple Hypotheses
TLDR
A strong connection between the derivatives of the cost function with respect to the coefficients and the detection/estimation errors of the sequential procedure is derived and it is shown that for suitably chosen cost coefficients the solutions of the constrained and the unconstrained problem coincide. Expand
Fading Boundaries: On a Nonparametric Variant of the Kiefer--Weiss Problem.
A nonparametric variant of the Kiefer--Weiss problem is proposed and investigated. In analogy to the classical Kiefer--Weiss problem, the objective is to minimize the maximum expected sample size ofExpand
Minimax Robust Detection: Classic Results and Recent Advances
TLDR
This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses, and an outlook on robust detection beyond the minimax principle. Expand
On Optimal Quantization in Sequential Detection
The problem of designing optimal quantization rules for sequential detectors is investigated. First, it is shown that this task can be solved within the general framework of active sequentialExpand

References

SHOWING 1-10 OF 73 REFERENCES
A Linear Programming Approach to Sequential Hypothesis Testing
Abstract Under some mild Markov assumptions it is shown that the problem of designing optimal sequential tests for two simple hypotheses can be formulated as a linear program. This result is derivedExpand
Almost optimal sequential tests of discrete composite hypotheses
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are basedExpand
Minimax Sequential Tests for Many Composite Hypotheses. II
The problem of sequential testing of many composite hypotheses is considered. Each hypothesis is described by the density function of observations that depends on a parameter from one of disjointExpand
Nearly Minimax One-Sided Mixture-Based Sequential Tests
Abstract We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider twoExpand
On Robustifying of the Sequential Probability Ratio Test for a Discrete Model under "Contaminations"
The problem of robustifying of the sequential probability ratio test is considered for a discrete hypothetical model. Exact values for error prob- abilities and for conditional expected sample sizesExpand
Robust statistics: a selective overview and new directions
Classical statistics relies largely on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are derived under theseExpand
Sequential Analysis: Hypothesis Testing and Changepoint Detection
Sequential Analysis: Hypothesis Testing and Changepoint Detection systematically develops the theory of sequential hypothesis testing and quickest changepoint detection. It also describes importantExpand
Minimax Robust Quickest Change Detection
TLDR
A robust version of these quickest change detection problems is considered when the pre-change and post-change distributions are not known exactly but belong to known uncertainty classes of distributions, such that the detection rule designed for the LFDs is optimal for the robust problem in a minimax sense. Expand
Minimax sequential tests of composite hypotheses on the drift of a Wiener process
A Wiener process with unknown drift parameter μ is, beginning at O, observed continuously and one has to decide between the hypotheses μ≤0 and μ>0. For loss functions of the form sμr and linear costExpand
On the Equivalence of $f$-Divergence Balls and Density Bands in Robust Detection
  • Michael Fauss, A. Zoubir, H. Poor
  • Mathematics, Computer Science
  • 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
  • 2018
TLDR
It is shown that for every pair of uncertainty sets of the f-divergence-ball type, a pair of Uncertainty Sets of the density-band type can be constructed, which implies that robust tests under $f$-diversion-ball uncertainty are also fixed sample size minimax optimal with respect to the equivalent density- band uncertainty sets. Expand
...
1
2
3
4
5
...