isoMean {logcondens}R Documentation

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

Description

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

sum_{i=1}^n (y_i - widehat 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

sum_{i=1}^n w_i(y_i - widehat g_i)^2 .

Usage

isoMean(y, w)

Arguments

y Vector (y_1, ..., y_n) of data points.
w Arbitrary vector (w_1, ..., w_n) of weights.

Value

Returns vector widehat g.

Author(s)

Kaspar Rufibach, kaspar.rufibach@stanford.edu,
http://www.stanford.edu/~kasparr

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.stat.unibe.ch/~duembgen

Examples

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

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

[Package logcondens version 1.0 Index]