On adaptive estimation of linear functionals
نویسندگان
چکیده
منابع مشابه
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...
متن کاملOn adaptive inverse estimation of linear functionals in Hilbert scales
We address the problem of estimating the value of a linear functional h f , xi from random noisy observations of y 1⁄4 Ax in Hilbert scales. Both the white noise and density observation models are considered. We propose an estimation procedure that adapts to unknown smoothness of x, of f , and of the noise covariance operator. It is shown that accuracy of this adaptive estimator is worse only b...
متن کاملAdaptive estimation of linear functionals under different performance measures
zi being independent and identically distributed standard normal random variables and M a finite or countably infinite index set. In particular, for these models minimax theory for mean squared error, confidence intervals and probabilistic error can all be precisely characterized by a modulus of continuity introduced by Donoho and Liu (1991). More specifically, for any linear functional T and c...
متن کاملAdaptive estimation of linear functionals by model selection
We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with respect to the Lp loss. An application to the problem of estimating a signal or its r derivative at a given point is developed and minimax rates are proved to hol...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2005
ISSN: 0090-5364
DOI: 10.1214/009053605000000633