logcondens (version 2.1.8)

isoMean: 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)

Value

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

Arguments

y

Vector \((y_1, \ldots, y_n)\) of data points.

w

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

Author

Kaspar Rufibach, ,
http://www.kasparrufibach.ch

Lutz Duembgen, ,
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')