论文标题
高斯非平稳过程的极端和投影密度估计的最大偏差
Extremes of Gaussian non-stationary processes and maximal deviation of projection density estimates
论文作者
论文摘要
在本文中，我们考虑了非平稳性高斯过程的至上的分布，并对该分布的渐近行为提出了新的理论结果。与以前在该领域中已知的事实不同，我们的主要定理产生了相应分布函数的渐近表示，并具有指数衰减的剩余项。该结果可以有效地用于研究基于Legendre多项式的投影密度估计值。更确切地说，我们构建了随附定律的序列，该法律近似于以多项式速率估算所考虑的估计值的最大偏差分布。此外，我们构建了密度的置信带，这些密度诚实，以多项式的速度对广泛的密度。
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main theorem yields the asymptotic representation of the corresponding distribution function with exponentially decaying remainder term. This result can be efficiently used for studying the projection density estimates, based, for instance, on Legendre polynomials. More precisely, we construct the sequence of accompanying laws, which approximates the distribution of maximal deviation of the considered estimates with polynomial rate. Moreover, we construct the confidence bands for densities, which are honest at polynomial rate to a broad class of densities.
