In non-asymptotic statistical inferences, variance-type parameters of sub-Gaussian distributions play a crucial role. However, direct estimation of these parameters based on the empirical moment generating function (MGF) is infeasible. To this end, we recommend using a sub-Gaussian intrinsic moment norm [Buldygin and Kozachenko (2000), Theorem 1.3] through maximizing a series of normalized moments. Importantly, the recommended norm can not only recover the exponential moment bounds for the corresponding MGFs, but also lead to tighter Hoeffding's sub-Gaussian concentration inequalities. In practice, {\color{black} we propose an intuitive way of checking sub-Gaussian data with a finite sample size by the sub-Gaussian plot}. Intrinsic moment norm can be robustly estimated via a simple plug-in approach. Our theoretical results are applied to non-asymptotic analysis, including the multi-armed bandit.
翻译:在非自然统计推断中,亚高加索地区分布的差异类型参数起着关键作用。 但是,根据经验时刻生成功能直接估算这些参数是不可行的。 为此,我们建议采用亚高加索地区固有的时间规范[Buldygin和Kozachenko(2000年),Theorem 1.3],通过最大限度地增加一系列正常时刻。 重要的是,建议的规范不仅能够恢复相应的MGFs的指数时刻界限,还能导致Hoffding的亚加西地区浓度不平等更加紧密。 实际上,我们建议用一种直观的方法,用亚加西地区绘图的有限样本大小来检查亚高加索地区的数据。通过简单的插头方法,可以强有力地估算出内刻时规范。我们的理论结果被用于非症状分析,包括多臂带。</s>