Monotone function estimator and its application

TL;DR

This paper introduces a new estimator for monotone functions, proves its convergence, constructs confidence intervals, and applies it to real-world wastewater data, addressing both i.i.d and dependent data scenarios.

Contribution

It proposes a novel monotone function estimator with proven convergence and practical confidence interval methods, including applications to dependent data.

Findings

Almost sure convergence of the estimator is established.

Confidence intervals and bands are constructed for i.i.d data.

Application demonstrated on urban wastewater treatment data.

Abstract

In this paper, the model $Y_i=g(Z_i),\ i=1,2,...,n$ with $Z_i$ being random variables with known distribution and $g(x)$ being unknown strictly increasing function is proposed and almost sure convergence of estimator for $g(x)$ is proved for i.i.d and short range dependent data. Confidence intervals and bands are constructed for i.i.d data theoretically and confidence intervals are introduced for short range dependent data through resampling. Besides, a test for equivalence of $g(x)$ to the desired function is proposed. Finite sample analysis and application of this model on an urban waste water treatment plant's data is demonstrated as well.