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Mathematical Methods of Statistics

, Volume 27, Issue 2, pp 83–102 | Cite as

Estimating the Index of Increase via Balancing Deterministic and Random Data

  • L. Chen
  • Y. Davydov
  • N. Gribkova
  • R. Zitikis
Article

Abstract

We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement errors. We prove consistency of the index and show how its rate of convergence is influenced by deterministic and random parts of the data. In particular, the obtained results suggest a frequency at which observations should be taken in order to reach any pre-specified level of estimation precision.We illustrate the index using data arising from purely deterministic and error-contaminated functions, which may or may not be monotonic.

Keywords

index of increase determinism randomness measurement errors smoothing cross validation 

2010 Mathematics Subject Classification

62G05 62G08 62G20 62P15 62P20 62P25 

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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.School of Math. and Statist. Sci.Western UniversityLondonCanada
  2. 2.Chebyshev Lab.St. Petersburg State Univ.St. PetersburgRussia
  3. 3.Faculty Math. and Mech.St. Petersburg State Univ.St. PetersburgRussia

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