Ancillary statistic

An ancillary statistic is a statistic that does not depend on the parameter being estimated and has a distribution that is independent of the parameter. It is often used as a tool for inference and estimation in statistical analysis. In the context of the given sentence, the misclosure vector is an example of an ancillary statistic.From: Handbook of Exponential and Related Distributions for Engineers and Scientists [2018], On the integrity of deformation monitoring [2020]

Event-Based Statistical Signal Processing

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Published in Marek Miskowicz, Event-Based Control and Signal Processing, 2018

Yasin Yilmaz, George V. Moustakides, Xiaodong Wang, Alfred O. Hero

In the presence of an ancillary statistic whose distribution does not depend on the parameters to be estimated, such as the regressor matrix Hn, the conditional covariance Cov(0n\Hn) can be used to assess the accuracy of the estimator more precisely than the (unconditional) covariance, which is in fact the mean of the former (i.e., Cov(0S) = E[COV(0„|Hn)]) [12,22]. Motivated by this fact, we propose to reformulate the problem in (20.54) conditioned on Hn, that is,

On the integrity of deformation monitoring

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Published in Geomatics, Natural Hazards and Risk, 2020

P. J. G. Teunissen, S. Zaminpardaz, C. C. J. M. Tiberius

As deformation monitoring involves statistical testing of multiple hypotheses, the whole chain of such complex decision making should be reflected in the computed integrity risk. Let the deformation monitoring multiple hypothesis testing problem therefore consist of hypotheses The null-hypothesis is considered to model the all-stable, zero-deformation case, while the other hypotheses model departures from . Then under , and in the presence of redundancy, a vector-function of the observables can be formed that has a fixed and known probability distribution. This vector-function is an ancillary statistic and it is known as the misclosure vector r (Teunissen, 2018). It is then by means of and its known probability density function (PDF), that the selection of the most likely hypothesis takes place. As such selection implies the partitioning of r in subsets r the testing procedure can be described as

Ancillary statistic

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Event-Based Statistical Signal Processing

On the integrity of deformation monitoring