# isoMean: Pool-Adjacent Violaters Algorithm: Least Square Fit under... In logcondens: Estimate a Log-Concave Probability Density from Iid Observations

## 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

 1 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

## Examples

  1 2 3 4 5 6 7 8 9 10 ## 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.