Estimating the index of increase via balancing deterministic and random data
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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.
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