Optimal Fixed Size Confidence Procedures for a Restricted Parameter Space

Zeytinoglu, M.; Mintz, Max

doi:10.1214/aos/1176346713

Cited by 22 publications

(16 citation statements)

References 2 publications

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“…While the theory addressed in this paper applies to many uncertainty classes, the primary focus of this paper is on asymmetric and/or multimodal models, that allow one to account for very general deviations from nominal sampling distributions. This paper extends earlier results in SDT and multi-sensor fusion obtained by [Zeytinoglu and Mintz, 1984], [Zeytinoglu and Mintz, 1988], and [McKendall and Mintz, 1988]. …”

Section: Introductionsupporting

confidence: 88%

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Robust Multi-Sensor Fusion: A Decision-Theoretic Approach

Kamberova

Mintz

1990

SPIE Proceedings

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Many tasks in active perception require that we be able to combine different information from a variety of sensors that relate to one or more features of the environment. Prior to combining these data, we must test our observations for consistency. The purpose of this paper is to examine sensor fusion problems for linear location data models using statistical decision theory (SDT). The contribution of this paper is the application of SDT to obtain: (i) a robust test of the hypothesis that data from different sensors are consistent; and (ii) a robust procedure for combining the data that pass this preliminary consistency test. Here, robustness refers to the statistical effectiveness of the decision rules when the probability distributions of the observation noise and the a priori position information associated with the individual sensors are uncertain. The standard linear location data model refers to observations of the form: Z = ϴ + V, where V represents additive sensor noise and ϴ denotes the "sensed" parameter of interest to the observer. While the theory addressed in this paper applies to many uncertainty classes, the primary focus of this paper is on asymmetric and/or multimodal models, that allow one to account for very general deviations from nominal sampling distributions. This paper extends earlier results in SDT and multi-sensor fusion obtained by [Zeytinoglu and Mintz, 1984], [Zeytinoglu and Mintz, 1988], and [McKendall and Mintz, 1988]. AbstractMany tasks in active perception require that we be able t o combine different information from a variety of sensors that relate to one or more features of the environment. Prior to combining these data, we must test our observations for consistency. The purpose of this paper is to examine sensor fusion problems for linear location data models using statistical decision theory (SDT). The contribution of this paper is the application of SDT to obtain: (i) a robust test of the hypothesis that data from different sensors are consistent; and (ii) a robust procedure for combining the data that pass this preliminary consistency test. Here, robustness refers to the statistical effectiveness of the decision rules when the probability distributions of the observation noise and the a priori position information associated with the individual sensors are uncertain. The standard linear location data model refers to observations of the form: Z = 8 + V, where V represents additive sensor noise and 9 denotes the "sensed" parameter of interest t o the observer. While the theory addressed in this paper applies to many uncertainty classes, the primary focus of this paper is on asymmetric and/or multimodal models, that allow one t o account for very general deviations from nominal sampling distributions. This paper extends earlier results in SDT and multi-sensor fusion obtained by [Zeytinoglu and Mintz, 19841, [Zeytinoglu and Mintz, 19881, and [McKendall and Mintz, 19881.

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Section: Introductionsupporting

confidence: 88%

“…R e m a r k 4.4 Theorem 4.2 extends the basic C-minimax results of [Zeytinoglu and Mintz, 19841 by allowing the inclusion of CDF's F that are asymmetric and/or multimodal.…”

Section: I N I M a X Rulesmentioning

confidence: 88%

Robust Multi-Sensor Fusion: A Decision-Theoretic Approach

Kamberova

Mintz

1990

SPIE Proceedings

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“…See [14] for a similar problem in which the largest possible scale is too large for the problem to reduce to standard estimation.) 0 [12] Zeytinoglu and Mintz, 1984 The standard-estimation problem of [12] has parameter space [-d, dJ. The noise distribution has a unimodal, symmetric density function and a monotone likelihood ratio.…”

Section: Features Of Decision Theorymentioning

confidence: 99%

“…[ 13} Zeytinoglu and Mintz, 1988 In [13], the standard-estimation problem of [12] is extended to robust estimation. The uncertainty class is a generalized uncertainty class for scale in which the boundary distribution 1 has a symmetric, unimodal density with a monotone likelihood ratio.…”

Section: Features Of Decision Theorymentioning

confidence: 99%

<title>Using robust statistics for sensor fusion</title>

McKendall

Mintz

1991

Sensor Fusion III: 3D Perception and Recognition

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The purpose of this article is to describe research in sensor fusion with statistical decision theory in the GRASP Lab, Department of Computer and Information Science, University of Pennsylvania. This article is thus a tutorial overview of the general research problem, the mathematical framework for the analysis, and the results of specific research problems. The intended audience for this article is a reader seeking a self-contained summary of the research. The prerequisite for understanding this article is faniiliarity with basic mathematical statistics.

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“…If the CDF F has a density function which is unimodal and symmetric about zero, then there exists a C-minimax rule 6' E A. Further, if F possesses a (strictly) mone tone likelihood ratio, then 6' is a minimax (admissible) Bayes rule.Proof SeeZeytinoglu and Mintz (1984).…”

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confidence: 99%

Robust fusion of location information

McKendall¹,

Mintz²

Proceedings. 1988 IEEE International Conference on Robotics and Automation

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The purpose of this paper is to examine a sensor fusion problem for location data using statistical decision theory (SDT). The contribution of this paper is the application of SDT to obtain: (i) a robust test of the hypothesis that data from different sensors is consistent; and (ii) a robust procedure for combining the data which pass this preliminary consistency test. Here, robustness refers to the statistical effectiveness of the decision rules when the probability distributions of the observation noise and the a priori position information associated with the individual sensors are uncertain. Location data refers to observations of the form: 2 = B + V, where V represents additive sensor noise and B denotes the "sensed" parameter of interest to the observer. While the theory developed in this paper applies to several uncertainty classes, the focus of this presentation is on r-contamination models, which d o w one to account for heavytailed deviations from nominal sampling distributions.

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Optimal Fixed Size Confidence Procedures for a Restricted Parameter Space

Cited by 22 publications

References 2 publications

Robust Multi-Sensor Fusion: A Decision-Theoretic Approach

Robust Multi-Sensor Fusion: A Decision-Theoretic Approach

<title>Using robust statistics for sensor fusion</title>

Robust fusion of location information

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