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MonotonicityTest: An R Package for Efficient Nonparametric Monotonicity Testing.

Dylan Huynh1, Layla Parast1

  • 1Statistics and Data Science University of Texas at Austin.

Observational Studies
|May 11, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces the MontonicityTest R package for nonparametric monotonicity testing. It provides an efficient implementation of a test for increasing conditional mean functions, crucial in econometrics and statistical analysis.

Keywords:
C++RRcppbootstrapkernel estimationmonotonicitynonparametricresidualtest

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Area of Science:

  • Statistics
  • Econometrics
  • Statistical Computing

Background:

  • Monotonicity testing is a fundamental problem in statistics, particularly relevant for time-series data analysis in econometrics.
  • Monotonicity is a common assumption underlying many statistical methods, relating to the estimation of true underlying functions from observed data.

Purpose of the Study:

  • Introduce and describe the R package MontonicityTest.
  • Implement a nonparametric test for the null hypothesis that the conditional mean function E(Y|X=x) is monotone increasing in x.
  • Make the previously unavailable Hall and Heckman (2000) test readily accessible to researchers.

Main Methods:

  • Leverages recursive least squares for the monotonicity test.
  • Implemented in C++ using the Rcpp package for computational efficiency.
  • Compares performance against a naive implementation to demonstrate reduced computational time.

Main Results:

  • The MontonicityTest package provides an efficient and accessible tool for monotonicity testing.
  • The implementation significantly reduces computational time compared to naive approaches.
  • Demonstrates the package's utility through an application to simulated diabetes clinical trial data.

Conclusions:

  • The MontonicityTest package offers a valuable resource for statistical and econometric analysis requiring monotonicity testing.
  • The efficient implementation facilitates the application of this important statistical condition in practice.
  • The package is ready for use in analyzing various datasets, including clinical trial data.