| essHist-package {essHist} | R Documentation |
The Essential Histogram
Description
Provide an optimal histogram, in the sense of probability density estimation and features detection, by means of multiscale variational inference. In other words, the resulting histogram servers as an optimal density estimator, and meanwhile recovers the features, such as increases or modes, with both false positive and false negative controls. Moreover, it provides a parsimonious representation in terms of the number of blocks, which simplifies data interpretation. The only assumption for the method is that data points are independent and identically distributed, so it applies to fairly general situations, including continuous distributions, discrete distributions, and mixtures of both. For details see Li, Munk, Sieling and Walther (2016) <arXiv:1612.07216>.
Details
| Package: | essHist |
| Type: | Package |
| Version: | 1.2.2 |
| Date: | 2019-05-10 |
| License: | GPL-3 |
Index:
essHistogram Compute the essential histogram checkHistogram Check any estimator by the multiscale confidence set genIntv Generate the system of intervals msQuantile Simulate the quantile of multiscale statistics dmixnorm Compute density function of Gaussian mixtures pmixnorm Compute distribution function of Gaussian mixtures rmixnorm Generate random number of Gaussian mixtures paramExample Output detailed parameters for some famous examples
Author(s)
Housen Li [aut, cre], Hannes Sieling [aut]
Maintainer: Housen Li <housen.li@outlook.com>
References
Li, H., Munk, A., Sieling, H., and Walther, G. (2016). The essential histogram. arXiv:1612.07216
Examples
# Simulate data
set.seed(123)
type = 'skewed_unimodal'
n = 500
y = rmixnorm(n, type = type)
# Compute the essential histogram
eh = essHistogram(y, plot = FALSE)
# Plot results
# compute oracle density
x = sort(y)
od = dmixnorm(x, type = type)
# compare with orcle density
plot(x, od, type = "l", xlab = NA, ylab = NA, col = "red", main = type)
lines(eh)
legend("topleft", c("Oracle density", "Essential histogram"),
lty = c(1,1), col = c("red", "black"))
##### Evaluate other method
set.seed(123)
# Data: mixture of Gaussians "harp"
n = 500
y = rmixnorm(n, type = 'harp')
# Oracle density
x = sort(y)
ho = dmixnorm(x, type = 'harp')
# R default histogram
h = hist(y, plot = FALSE)
# Check R default histogram to local multiscale constraints
b = checkHistogram(h, y, ylim=c(-0.1,0.16))
lines(x, ho, col = "red")
rug(x, col = 'blue')
legend("topright", c("R-Histogram", "Truth"), col = c("black", "red"), lty = c(1,1))