MonotonicityTest: An R Package for Efficient Nonparametric Monotonicity Testing

Monotonicity testing is a classic and longstanding problem in statistics, with particular importance in econometrics when analyzing data measured over time. More generally, monotonicity often underlies many statistical methods as a common condition, typically related to a true underlying function estimated from observed data. In this work, we introduce and describe the R package MontonicityTest which implements a nonparametric test of the null hypothesis that the conditional mean function $E(Y|X=x)$ is monotone increasing (non-decreasing) in x given observed data on ( $X,Y$ ). The test itself was introduced in Hall and Heckman (2000) but has thus far not been readily available. Our package leverages recursive least squares and is implemented in C++ using the Rcpp package, which significantly reduces computational time relative to a naive approach. We describe the package details and features, as well as illustrate the main functions with an application to simulated diabetes clinical trial data.