Pool-Adjacent Violaters Algorithm: Least Square Fit under Monotonicity Constraint
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.
isoMean(y, w)
y |
Vector (y_1, …, y_n) of data points. |
w |
Arbitrary vector (w_1, …, w_n) of weights. |
Returns vector \widehat g.
Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch
## 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')Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.