MULTISCALE SMOOTHING ERROR MODELS

A class of multiscale stochastic models based on scale-recursive dynam ics on trees has recently been introduced. These models are interestin g because they can be used to represent a broad class of physical phen omena and because they lead to efficient algorithms for estimation and likelihood calculation. In this paper, we provide a complete statisti cal characterization of the error associated with smoothed estimates o f the multiscale stochastic processes described by these models. In pa rticular, we show that the smoothing error is itself a multiscale stoc hastic process with parameters that can be explicitly calculated.