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Minimax testing of a composite null hypothesis defined via a quadratic functional in the model of regression
Nonparametric hypotheses testing sharp asymptotics separation rates minimax approach high-dimensional regression.
2012/9/17
We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadraticfunctional Q, the null hypothesis states tha...
Quadratic functional estimation in inverse problems
Gaussian sequence model inverse problem minimax upper bounds parametric rate Pinsker estimator projection estimator
2010/3/18
We consider in this paper a Gaussian sequence model of observations Yi, i ≥ 1
having mean (or signal) θi and variance σi which is growing polynomially like i
,γ > 0. This model describes a large pan...
Optimal adaptive estimation of a quadratic functional
Adaptation block thresholding quadratic functionals wavelets white noise model
2010/4/26
Adaptive estimation of a quadratic functional over both Besov
and Lp balls is considered. A collection of nonquadratic estimators
are developed which have useful bias and variance properties over
i...