Efficient estimation of linear functionals of principal components

Efficient Estimation of Linear Functionals of Abivariate Distribution with Equal

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). ...

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...

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...

Computationally Efficient Robust Estimation of Sparse Functionals

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse functionals, and provide a computationally and statistically efficient algor...