unimonotone {monotone}

Unimodal Monotone Regression Function

Description

unimonotone performs unimodal monotone 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) for both isotonic and antitonic regression, and the prefix isotonic regression approach (Stout, 2008) with additional lookaheads and progressive error sum-of-squares computation.

Usage

unimonotone(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 umbrella order.

References

Bril G, Dykstra R, Pillers C, Robertson T (1984). Algorithm AS 206: isotonic regression in two independent variables. Journal of the Royal Statistical Society. Series C (Applied Statistics), 33(3), 352-357. URL https://www.jstor.org/stable/pdf/2347723.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>)

Stout, Q.F. (2008). Unimodal Regression via Prefix Isotonic Regression. Computational Statistics and Data Analysis, 53, pp. 289-297. URL https://doi:10.1016/j.csda.2008.08.005

Turner, T.R. and Wollan, P.C. (1997). Locating a maximum using isotonic regression. Computational statistics and data analysis, 25(3), pp. 305-320. URL https://doi.org/10.1016/S0167-9473(97)00009-1

Turner, T.R. (2019). Iso: Functions to Perform Isotonic Regression. R package version 0.0-18. URL https://cran.r-project.org/package=Iso

Examples

y <- c( 0.0,61.9,183.3,173.7,250.6,238.1,292.6,293.8,268.0,285.9,258.8,
297.4,217.3,226.4,170.1,74.2,59.8,4.1,6.1 )
x <- unimonotone( y )
print( x )