logcondens (version 2.0.6)

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)

Arguments

y

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

w

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

Value

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

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')