| monotone {monotone} | R Documentation |
Monotone Regression Function
Description
monotone performs simple linear ordered monotone or isotonic regression.
The function follows the up-and-down-blocks implementation (Kruskal, 1964)
of the pool-adjacent-violators algorithm (Ayer, Brunk, Ewing, Reid, and Silverman, 1955)
with additional lookaheads (Busing, 2022).
Usage
monotone(x, w = rep(1, length(x)))
Arguments
x |
a real-valued vector. |
w |
a real-valued vector with positive weights (default a vector with ones). |
Details
Error checking on x or w is not present.
Value
Returns a real-valued vector with values of x in increasing order.
References
Ayer M., H.D. Brunk, G.M. Ewing, W.T. Reid, and E. Silverman (1955). An empirical distribution function for sampling with incomplete information. The Annals of Mathematical Statistics, pp. 641-647. URL https://www.jstor.org/stable/pdf/2236377.pdf.
Busing, F.M.T.A. (2022). Monotone Regression: A Simple and Fast O(n) PAVA Implementation. Journal of Statistical Software, Code Snippets, 102 (1), pp. 1-25. (<doi:10.18637/jss.v102.c01>)
Kruskal, J.B. (1964). Nonmetric multidimensional scaling: a numerical method. Psychometrika, 29(2), pp. 115-129. URL http://cda.psych.uiuc.edu/psychometrika_highly_cited_articles/kruskal_1964b.pdf.
Examples
y <- c( 8, 4, 8, 2, 2, 0, 8 )
x <- monotone( y )
print( x )