We develop a new model selection method for the adaptive robust efficient nonparametric signal estimation observed with impulse noise which is defined by the general non Gaussian L\'evy processes. On the basis of the developed method, we construct the estimation procedures which are analyzed in two settings: in non asymptotic and asymptotic ones. For the first time for such models we show non asymptotic sharp oracle inequalities for the quadratic and for the robust risks, i.e. we show that the constructed procedures are optimal in the sharp oracle inequalities sense. Next, by making use of the obtained oracle inequalities, we provide the asymptotic efficiency property for the developed estimation methods in the adaptive setting when the signal/noise ratio goes to infinity. We apply the developed model selection methods for the signals number detection problem in multi-path information transmission.

中文翻译：

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使用小 Lévy 噪声观察到的稳健高效信号处理的模型选择

我们开发了一种新的模型选择方法，用于通过一般非高斯 L'evy 过程定义的脉冲噪声观察到的自适应鲁棒高效非参数信号估计。在开发的方法的基础上，我们构建了在两种情况下分析的估计程序：非渐近和渐近。对于这样的模型，我们第一次展示了二次和稳健风险的非渐近尖锐 oracle 不等式，即我们表明构建的过程在尖锐 oracle 不等式意义上是最优的。接下来，通过利用获得的 oracle 不等式，当信噪比趋于无穷大时，我们为自适应设置中开发的估计方法提供渐近效率属性。