The monotone package contains a fast up-and-down-blocks implementation for the pool-adjacent-violators algorithm 
  for simple linear ordered monotone regression, including two spin-off functions
  for unimodal and bivariate monotone regression (see <doi:10.18637/jss.v102.c01>).

Nonparametric estimation and inference of a non-decreasing monotone hazard
    ratio from a right censored survival dataset.  The
    estimator is based on a generalized Grenander typed estimator, and the
    inference procedure relies on direct plugin estimation of a first order derivative.  More
    details please refer to the paper "Nonparametric inference under a monotone
    hazard ratio order" by Y. Wu and T. Westling (2023) <doi:10.1214/23-EJS2173>.

Test for monotonicity in financial variables sorted by portfolios. It is conventional practice in empirical research to form portfolios of assets ranked by a certain sort variable. A t-test is then used to consider the mean return spread between the portfolios with the highest and lowest values of the sort variable. Yet comparing only the average returns on the top and bottom portfolios does not provide a sufficient way to test for a monotonic relation between expected returns and the sort variable. This package provides nonparametric tests for the full set of monotonic patterns by Patton, A. and Timmermann, A. (2010) <doi:10.1016/j.jfineco.2010.06.006> and compares the proposed results with extant alternatives such as t-tests, Bonferroni bounds, and multivariate inequality tests through empirical applications and simulations.

Implements nonparametric bootstrap tests for detecting monotonicity
  in regression functions from Hall, P. and Heckman, N. (2000) <doi:10.1214/aos/1016120363>
  Includes tools for visualizing results using Nadaraya-Watson kernel regression and supports 
  efficient computation with 'C++'.

Estimates monotone regression and variance functions in a nonparametric model, based on Dette, Holger, Neumeyer, and Pilz (2006) <doi:10.3150/bj/1151525131>.