bimonotone {monotone}

Bivariate Monotone Regression Function

Description

bimonotone performs bivariate monotone regression. The function uses the up-and-down-blocks implementation (Kruskal, 1964) of the pool-adjacent-violators algorithm (Ayer, Brunk, Ewing, Reid, and Silverman, 1955), with additional lookaheads, repeatedly, for both rows and columns, until convergence.

Usage

bimonotone(
  x,
  w = matrix(1, nrow(x), ncol(x)),
  maxiter = 65536,
  eps = 1.49011611938477e-08
)

Arguments

x

a real-valued matrix.

w

a real-valued matrix with positive weights (default a matrix with ones).

maxiter

maximum number of iterations (default = 65536)

eps

precision of estimates (default = 1.4901161193847656e-08)

Details

Error checking on x, w, maxiter, or eps is not present.

Value

Returns a real-valued matrix with values of both rows and columns of x in monotone 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>)

Dykstra R.L., Robertson T. (1982). An algorithm for isotonic regression for two or more independent variables. The Annals of Statistics, 10(3), 708-716. URL https: //projecteuclid.org/download/pdf_1/euclid.aos/1176345866.

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

G <- matrix( c( 1, 5.2, 0.1, 0.1, 5, 0, 6, 2, 3, 5.2, 5, 7, 4, 5.5, 6, 6 ), 4, 4 )
print( G )
H <- bimonotone( G )
print( H )
y <- c( 8, 4, 8, 2, 2, 0, 8 )
x <- bimonotone( as.matrix( y ) )
print( x )
x <- bimonotone( t( as.matrix( y ) ) )
print( x )