The former process is sometimes called a Rao-Blackwellization process.
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check here . However such a ”Rao-Blackwellization” of an unbiased estimator does not necessarily provide a UMVU (uniformly minimum variance unbiased) estimator. the statistic produces a UMVU estimator. These concepts are more difficult for a finite population. Example in robot mapping:The joint distribution robot path $x_{0:t}$ and the landmarks $m_{1:M}$ can be represented by individual sample of the robot paths and the corresponding conditional probability of the landmarks given the robot path:The state of the particle filter in FastSLAM becomes the robot path only $x_{1:t}$, rather than the higher dimensional counterpart, $x_{1:t}, m1, \dots, m_M$.

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Unable to display preview. This is a preview of subscription content, access via your institution. r. With Rao-Blackwellization, we can factor the joint distribution to exploit dependencies between variables.

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This way the particle filtering becomes more efficient. Correspondence to
George A. DOI: https://doi. That is because it requires more samples to sufficiently approximate the joint distribution of all the state variables. © 2012 The Author(s)DOI: https://doi.

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Unable to display preview. Download preview PDF. check these guys out provides a powerful tool for particle filter in high dimensional space. org/10.

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Hence the class of unbiased estimators which are functions of a sufficient statistic constitutes an essentially complete class. t. Seber . The theory is also applied to selecting networks without replacement, and the question of ignoring information from labels is considered.

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variance by an unbiased estimator which is a function of a sufficient statistic. 1007/978-3-642-33657-7_3Published: 23 October 2012
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33656-0
Online ISBN: 978-3-642-33657-7eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)The Rao-Blackwell theorem says that if we want an estimator with small MSE we can confine our search to estimators which are functions of the sufficient statistic. – Richard Weber, Statistics (Part IB) Lecture NotesTo give a simple example:If we want to approximate the joint distribution $p(a,b)$ with samples, a sampler that samples a from $p(a)$ and then determines b analytically conditioned on a, $p(b \vert a)$, is no worse than a sampler that samples directly from the joint distribution p(a, b). The Rao-Blackwell theorem can be applied to unbiased estimators to provide more efficient estimators. Closed form expressions for these and related estimators are discussed.

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This is a preview of subscription content, access via your institution. r. F. It asserts that any unbiased estimator is improved w.

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© 1994 Springer-Verlag New York, Inc. The Rao-Blackwell theorem is one of the most important theorems in mathematical statistics. More specifically speaking, particle filter becomes inefficient when the state is high-dimensional. Download preview PDF. 1007/978-1-4612-2644-4_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94216-2
Online ISBN: 978-1-4612-2644-4eBook Packages: Springer Book ArchiveThis chapter summarizes some foundational theory for adaptive sampling methods. .

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