isoMean: Pool-Adjacent Violaters Algorithm: Least Square Fit under...

Description Usage Arguments Value Author(s) Examples

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

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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@gmail.com,
http://www.kasparrufibach.ch

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

Examples

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## 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')

logcondens documentation built on May 2, 2019, 6:11 a.m.