Probability Inequalities
Probability Inequalities
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DOI：
10.1007/1-84628-052-4_9
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Jovanović;S. Gerhold
中科院分区：
文献类型：
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作者：
M. Jovanović;S. Gerhold
本章讨论了概率估计中有限样本量的问题，即所谓的样本复杂度。在这种情况下，主要目标是严格分析第7章中介绍的有限样本量的概率估计的可靠性。这个问题在不确定系统和控制的随机算法的发展中是至关重要的，并且与基于大数定律的渐近方法有明显区别。具体来说，这一章包括Markov不等式、Chebychev不等式和Hoeffding不等式。随后导出了加性切尔诺夫界和乘性切尔诺夫界，并研究了极值估计的样本复杂度。
This chapter addresses the issue of finite sample size in probability estimation, that is, the so-called sample complexity. The main objective in this context is to analyze rigorously the reliability of the probabilistic estimates introduced in Chap. 7 , for a finite sample size. This issue is crucial in the development of randomized algorithms for uncertain systems and control, and makes a clear distinction from the asymptotic methods which are instead based on the laws of large numbers. Specifically, the chapter includes Markov, Chebychev and Hoeffding inequalities. The additive and multiplicative Chernoff bounds are subsequently derived and the sample complexity for estimation of extrema is also studied.