Nason, Guy

This article introduces a new class of location estimators by applying an existingmeasure of location to a set of multiscale means computed on the order statistics of a data set.Class members are shown to have interesting and desirable properties such as: the member usingthe geometric mean is always sandwiched between the geometric and arithmetic means.The member using the median reduces to a simple form, the guard estimator,which is the median of three quantities: the sample mean and two guard values based on two or four orderstatistics nearest the median. The guard estimator is unbiased, consistent (at least for symmetric distributions),computable in linear time, does not require tuning parameters and simulations suggest thatit achieves high efficiency: almost matching the mean or median's better efficiency under different distributions.Guard's finite sample breakdown point demonstrates that it is highly robust even for small samplesand matches the median's breakdown value asymptotically. Two examples exhibit the new locationmeasures in action: one provides confirmation of a robust approach to establishing whetherShoshoni leather goods were designed to the `Golden Ratio' standard; the other comparesfour functional measures of location for the Aberporth wind speed series.The new class of location estimators is inspired by the member that uses the geometric mean which arises naturally from a theoretical analysis of multiscale variance stabilization (MVS) techniques.The articleintroduces maximum likelihood approaches for MVS techniques for independently andidentically distributed dataand sheds theoretical light on MVS by presenting analytical formulae for their Jacobians, a key componentof the likelihood.The MVS techniques are shown empirically to compare favourably to the well-known Box-Coxtransform, but do not dominate it

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New Class of Location Measures, the Guard Estimator and Connections to Multiscale Variance Stabilization

https://research-information.bris.ac.uk/files/57794074/hfbc3.pdf

New Class of Location Measures, the Guard Estimator and Connections to Multiscale Variance Stabilization

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