isoMean {logcondens}

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

Description

Fits a vector \widehat {\bold{g}} with nondecreasing components to the data vector {\bold{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 {\bold{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, \ldots, y_n) of data points.

w

Arbitrary vector (w_1, \ldots, w_n) of weights.

Value

Returns vector \widehat {\bold{g}}.

Author(s)

Kaspar Rufibach, [e-mail],
http://www.kasparrufibach.ch

Lutz Duembgen, [e-mail],
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/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')