rebmix (version 2.12.0)

demix-methods: Empirical Density Calculation

Description

Returns the data frame containing observations \(\bm{x}_{1}, \ldots, \bm{x}_{n}\) and empirical densities \(f_{1}, \ldots, f_{n}\) for the kernel density estimation or k-nearest neighbour or bin means \(\bar{\bm{x}}_{1}, \ldots, \bar{\bm{x}}_{v}\) and empirical densities \(f_{1}, \ldots, f_{v}\) for the histogram preprocessing. Vectors \(\bm{x}\) and \(\bar{\bm{x}}\) are subvectors of \(\bm{y} = (y_{1}, \ldots, y_{d})^{\top}\) and \(\bar{\bm{y}} = (\bar{y}_{1}, \ldots, \bar{y}_{d})^{\top}\).

Usage

# S4 method for REBMIX
demix(x = NULL, pos = 1, variables = expression(1:d), ...)
## ... and for other signatures

Arguments

x

see Methods section below.

pos

a desired row number in x@summary for which the empirical densities are calculated. The default value is 1.

variables

a vector containing indices of variables in subvectors \(\bm{x}\) or \(\bar{\bm{x}}\). The default value is 1:d.

…

currently not used.

Methods

signature(x = "REBMIX")

an object of class REBMIX.

signature(x = "REBMVNORM")

an object of class REBMVNORM.

References

M. Nagode and M. Fajdiga. The rebmix algorithm for the univariate finite mixture estimation. Communications in Statistics - Theory and Methods, 40(5):876-892, 2011a. https://doi.org/10.1080/03610920903480890. M. Nagode and M. Fajdiga. The rebmix algorithm for the multivariate finite mixture estimation. Communications in Statistics - Theory and Methods, 40(11):2022-2034, 2011b. https://doi.org/10.1080/03610921003725788. M. Nagode. Finite mixture modeling via REBMIX. Journal of Algorithms and Optimization, 3(2):14-28, 2015. https://doi.org/10.5963/JAO0302001.

Examples

# NOT RUN {
# Generate simulated dataset.

n <- c(15, 15)

Theta <- new("RNGMIX.Theta", c = 2, pdf = rep("normal", 3))

a.theta1(Theta, 1) <- c(10, 20, 30)
a.theta1(Theta, 2) <- c(3, 4, 5)
a.theta2(Theta, 1) <- c(3, 2, 1)
a.theta2(Theta, 2) <- c(15, 10, 5)

simulated <- RNGMIX(Dataset.name = paste("simulated_", 1:4, sep = ""),
  rseed = -1,
  n = n,
  Theta = a.Theta(Theta))

# Number of classes or nearest neighbours to be processed.

K <- c(as.integer(1 + log2(sum(n))), # Minimum v follows Sturges rule.
  as.integer(10 * log10(sum(n)))) # Maximum v follows log10 rule.

# Estimate number of components, component weights and component parameters.

simulatedest <- REBMIX(model = "REBMVNORM",
  Dataset = a.Dataset(simulated),
  Preprocessing = "h",
  cmax = 4,
  Criterion = "BIC",
  pdf = c("n", "n", "n"),
  K = K[1]:K[2])

# Preprocess simulated dataset.

f <- demix(simulatedest, pos = 3, variables = c(1, 3))

f

# Plot finite mixture.

opar <- plot(simulatedest, pos = 3, nrow = 3, ncol = 1)

par(usr = opar[[2]]$usr, mfg = c(2, 1))

text(x = f[, 1], y = f[, 2], labels = format(f[, 3], digits = 3), cex = 0.8, pos = 1)
# }