MonotonicityTest: An R Package for Efficient Nonparametric Monotonicity Testing

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.