Publication

Optimal Interpolation of Fractional Brownian Motion Given Its Noisy Samples

Michaël Unser, Thierry Blu
2006
Conference Papers

Abstract

We consider the problem of estimating a fractional Brownian motion known only from its noisy samples at the integers. We show that the optimal estimator can be expressed using a digital Wiener-like filter followed by a simple time-variant correction accounting for nonstationarity. Moreover, we prove that this estimate lives in a symmetric fractional spline space and give a practical implementation for optimal upsampling of noisy fBm samples by integer factors.

Official source

https://infoscience.epfl.ch/entities/publication/6e6c6df5-9a65-4c7b-a9e2-b03450b26855

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Michaël Unser, Thierry Blu
2006
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6e6c6df5-9a65-4c7b-a9e2-b03450b26855

About this result

Related concepts (12)

Minimum-variance unbiased estimator

In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter. For practical statistics problems, it is important to determine the MVUE if one exists, since less-than-optimal procedures would naturally be avoided, other things being equal. This has led to substantial development of statistical theory related to the problem of optimal estimation.

Bias of an estimator

In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased; see bias versus consistency for more.

Invariant estimator

In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity. It is a way of formalising the idea that an estimator should have certain intuitively appealing qualities. Strictly speaking, "invariant" would mean that the estimates themselves are unchanged when both the measurements and the parameters are transformed in a compatible way, but the meaning has been extended to allow the estimates to change in appropriate ways with such transformations.

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