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.
Translated title of the contributionОценивание индекса роста через балансирование детерминированных и случайных данных
Original languageEnglish
Pages (from-to)83-102
Number of pages20
JournalMathematical Methods of Statistics
Volume27
Issue number2
DOIs
StatePublished - 1 Apr 2018

    Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

    Research areas

  • cross validation, determinism, index of increase, measurement errors, randomness, smoothing, PRICE UNCERTAINTY, RISK, N-BOOTSTRAP, UTILITY, FIRM, PROSPECT-THEORY

ID: 34784842