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++'. Tutorials and shiny application demo are 
  available at <https://www.laylaparast.com/monotonicitytest> and <https://parastlab.shinyapps.io/MonotonicityTest>.

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

Computes Monte Carlo standard errors for summaries of Monte Carlo output. Summaries and their standard errors are based on columns of Monte Carlo simulation output. Dennis D. Boos and Jason A. Osborne (2015) <doi:10.1111/insr.12087>.

Simplifies Monte Carlo simulation studies by automatically 
             setting up loops to run over parameter grids and parallelising
             the Monte Carlo repetitions. It also generates LaTeX tables.

Monte Carlo simulation allows testing different conditions given to the correct structural equation models. This package runs Monte Carlo simulations under different conditions (such as sample size or normality of data). Within the package data sets can be simulated and run based on the given model.
  First, continuous and normal data sets are generated based on the given model. Later Fleishman's power method (1978) <DOI:10.1007/BF02293811> is used to add non-normality if exists. 
  When data generation is completed (or when generated data sets are given) model test can also be run.
  Please cite as "Orçan, F. (2021). MonteCarloSEM: An R Package to Simulate Data for SEM. International Journal of Assessment Tools in Education, 8 (3), 704-713."