For the Gaussian sequence model, we obtain nonasymptotic minimax rates of estimation of the linear, quadratic and the ℓ2-norm functionals on classes of sparse vectors and construct optimal estimators ...

The conventional linear/quadratic/Gaussian assumptions are modified in that minimisation of the expectation of cost G defined by (2) is replaced by minimisation of the criterion function (5). The ...

Examples of Nonparametric Statistics In the first example, consider a financial analyst who wishes to estimate the value at risk (VaR) of an investment. The analyst gathers earnings data from ...