Pool-Adjacent Violaters Algorithm: Least Square Fit under Monotonicity Constraint

Description

Fits a vector hat g with nondecreasing components to the data vector y such that

∑_{i=1}^n (y_i - hat g_i)^2

is minimal (pool - adjacent - violators algorithm). In case a weight vector with positive entries (and the same size as y) is provided, the function produces an isotonic vector minimizing

∑_{i=1}^n w_i(y_i - hat g_i)^2.

Usage

isoMean(y, w)

Arguments

Value

Returns vector widehat g.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.stat.unibe.ch/content/staff/personalhomepages/duembgen/index_eng.html

Examples

## simple regression model
n <- 50
x <- sort(runif(n, 0, 1))
y <- x ^ 2 + rnorm(n, 0, 0.2)
s <- seq(0, 1, by = 0.01)
plot(s, s ^ 2, col = 2, type = 'l', xlim = range(c(0, 1, x)), 
    ylim = range(c(0, 1 , y))); rug(x)

## plot pava result
lines(x, isoMean(y, rep(1 / n, n)), type = 's')

Results