Efficient Estimation of Linear Functionals in Emission Tomography

Efficient Estimation of Linear Functionals in Emission Tomography

In emission tomography, the spatial distribution of a radioactive tracer is estimated from a finite sample of externally detected photons. We present an algorithm-independent theory of statistical accuracy attainable in emission tomography that makes minimal assumptions about the underlying image. Let f denote the tracer density as a function of position (i.e., f is the image being estimated). ...

Minimax Estimation of Linear Functionals, Particularly in Nonparametric Regression and Positron Emission Tomography

Often it is required to estimate a linear functional of a function f given observations of some kind from f . We consider the linear minimax estimation of a bounded linear functional T with respect to the mean square error loss function over a certain class of functions F defined by means of a semi-norm, which in practice usually provides some restriction on roughness. We review the remarkable ...

Asymptotically Efficient Estimation of Linear Functionals in Inverse Regression Models

In this paper we will discuss a procedure to improve the usual estimator of a linear functional of the unknown regression function in inverse nonparametric regression models. In Klaassen et al. (2001) it has been proved that this traditional estimator is not asymptotically efficient (in the sense of the Hájek Le Cam convolution theorem) except, possibly, when the error distribution is normal. S...

Efficient Estimation of Linear Functionals of Abivariate Distribution with Equal

On Adaptive Estimation of Linear Functionals

A detailed analysis of minimax estimates of arbitrary linear functionals based on infinite dimensional Gaussian models has been provided by Donoho and Liu. In particular it has been shown that if the parameter space is convex then linear estimates can always be found which have maximum mean squared error within a small constant multiple of the minimax value. These linear estimates do however ha...