Assessing Monotonicity: An Approach Based on Transformed Order Statistics

IF 0.8 Q3 STATISTICS & PROBABILITY
Aleksandr Chen, Nadezhda Gribkova, Ričardas Zitikis
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引用次数: 0

Abstract

In a number of research areas, such as non-convex optimization and machine learning, determining and assessing regions of monotonicity of functions is pivotal. Numerically, it can be done using the proportion of positive (or negative) increments of transformed ordered inputs. When the number of inputs grows, the proportion tends to an index of increase (or decrease) of the underlying function. In this paper, we introduce a most general index of monotonicity and provide its interpretation in all practically relevant scenarios, including those that arise when the distribution of inputs has jumps and flat regions, and when the function is only piecewise differentiable. This enables us to assess monotonicity of very general functions under particularly mild conditions on the inputs.

Abstract Image

评估单调性:基于变换阶次统计的方法
摘要 在非凸优化和机器学习等多个研究领域,确定和评估函数的单调性区域至关重要。在数值上,可以利用变换有序输入的正(或负)增量比例来实现。当输入的数量增加时,该比例就会趋向于基础函数的增加(或减少)指数。在本文中,我们引入了一种最通用的单调性指数,并在所有与实际相关的情况下对其进行了解释,包括输入分布存在跳跃和平坦区域时,以及函数仅为片断微分时出现的情况。这使我们能够在输入条件特别温和的情况下评估非常一般的函数的单调性。
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来源期刊
Mathematical Methods of Statistics
Mathematical Methods of Statistics STATISTICS & PROBABILITY-
CiteScore
0.60
自引率
0.00%
发文量
2
期刊介绍: Mathematical Methods of Statistics  is an is an international peer reviewed journal dedicated to the mathematical foundations of statistical theory. It primarily publishes research papers with complete proofs and, occasionally, review papers on particular problems of statistics. Papers dealing with applications of statistics are also published if they contain new theoretical developments to the underlying statistical methods. The journal provides an outlet for research in advanced statistical methodology and for studies where such methodology is effectively used or which stimulate its further development.
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