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We propose a new test, based on model selection methods, for testing that the expectation of a Gaussian vector with n independent components belongs to a linear subspace of $\R^{n}$ against a nonparametric alternative. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative. The properties of the test are nonasymptotic and we prove that the test is rate optimal [up to a possible log(n…

通过模型选择自适应估计二次泛函AI 解读

We consider the problem of estimating $\|s\|^2$ when $s$ belongs to some separable Hilbert space and one observes the Gaussian process $Y(t) = \langles, t\rangle + \sigmaL(t)$, for all $t \epsilon \mathbb{H}$,where $L$ is some Gaussian isonormal process. This framework allows us in particular to consider the classical “Gaussian sequence model” for which $\mathbb{H} = l_2(\mathbb{N}*)$ and $L(t) = \sum_{\lambda\geq1}t_{\lambda}\varepsilon_{\lambda}$, where $(\varepsilon_{\lambda})_{\lambda\geq1}$…