TY - JOUR

T1 - Assessing Monotonicity: An Approach Based on Transformed Order Statistics

AU - Chen, Aleksandr

AU - Грибкова, Надежда Викторовна

AU - Zitikis, Ričardas

N1 - Chen, A., Gribkova, N. & Zitikis, R. Assessing Monotonicity: An Approach Based on Transformed Order Statistics. Math. Meth. Stat. 33, 79–94 (2024). https://doi.org/10.3103/S1066530724700054

PY - 2024/4/25

Y1 - 2024/4/25

N2 - 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.

AB - 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.

KW - monotonicity

KW - function

KW - index of increase

KW - order statistics

KW - function

KW - index of increase

KW - monotonicity

KW - order statistic

UR - https://www.mendeley.com/catalogue/2e1b29d1-1727-34e9-b7c2-d17ef631c885/

U2 - 10.3103/S1066530724700054

DO - 10.3103/S1066530724700054

M3 - Article

VL - 33

SP - 79

EP - 94

JO - Mathematical Methods of Statistics

JF - Mathematical Methods of Statistics

SN - 1066-5307

IS - 1

ER -