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 ...

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 ...

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 ...