Sequential estimation

In statistics, sequential estimation refers to estimation methods in sequential analysis where the sample size is not fixed in advance. Instead, data is evaluated as it is collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. The generic version is called optimal Bayesian Estimator, which is the theoretical underpinning for every sequential estimator (but cannot be instantiated directly). It includes a Markov-Process for the state propagation and measurement process for each state, which yields some typical statistical independence relations. From that, the Kalman Filter (and its variants), the particle filter, the histogram filter and others can be derived. It depends on the models, which one to use and requires experience to chose the right one. In most cases, the goal is to estimate the state sequence from the measurements. In other cases, one can use the description to estimate the parameters of a noise process for example. One can also accumulate the unmodeled statistical behavior (typically called innovation) over time and compare it with a threshold, which then corresponds to the aforementioned stopping criterion.

If there is a dependence of each state on an overall entity (e.g. a map or a an overall state variable), one typically uses SLAM (simultenous localization and mapping) techniques, which includes the sequential estimator as a special case.

See also

• Sequential Probability Ratio Test
• Testimator

References

• Thomas S. Ferguson (1967) Mathematical statistics: A decision theoretic approach., Academic Press. ISBN 0-12-253750-5
• Wald, Abraham (1947). Sequential Analysis. New York: John Wiley and Sons. ISBN 0-471-91806-7. See Dover reprint: ISBN 0-486-43912-7 {{cite book}}: ISBN / Date incompatibility (help)