mixMPHD {MixSemiRob}

Semiparametric Mixture Model by Minimizing Profile Hellinger Distance

Description

‘mixMPHD’ provides an efficient and robust estimation of a mixture of unknown location-shifted symmetric distributions using a semiparamatric method (Wu et al., 2017). As of version 1.1.0, 'mixMPHD' supports a two-component model, which is defined as

h(x;\boldsymbol{\theta},f) = \pi f(x-\mu_1)+(1-\pi)f(x-\mu_2),

where \boldsymbol{\theta}=(\pi,\mu_1,\mu_2)^{\top} is the parameter to estimate, f is an unknown density function that is symmetric at zero. The parameters are estimated by minimizing the profile Hellinger distance (MPHD) between the parametric model and a non-parametric density estimate.

Usage

mixMPHD(x, sigma.known = NULL, ini = NULL)

Arguments

x

a vector of observations.

sigma.known

standard deviation of one component (if known). Default is NULL.

ini

initial values for the parameters. Default is NULL, which obtains the initial values using the mixOnekn function. It can be a list with the form of list(mu, pi, sigma), where mu is a vector of component means, pi is a vector of component mixing proportions, sigma is a vector of component standard deviations.

Value

A list containing the following elements:

lik

final likelihood.

pi

estimated mixing proportion.

sigma

estimated component standard deviation. Only returned when sigma.known is not provided.

mu

estimated component mean.

run

total number of iterations after convergence.

References

Wu, J., Yao, W., and Xiang, S. (2017). Computation of an efficient and robust estimator in a semiparametric mixture model. Journal of Statistical Computation and Simulation, 87(11), 2128-2137.

See Also

mixOnekn for initial value calculation.

Examples

# Model: X ~ 0.3*N(0, 1) + 0.7*N(3, 1)
set.seed(4)
n = 100
p = 0.3
n1 = rbinom(1, n, p)
sigma1 = 1
sigma2 = 1
x1 = rnorm(n1, mean = 0, sd = sigma1)
x2 = rnorm(n - n1, mean = 3, sd = sigma2)
x = c(x1, x2)
ini = mixOnekn(x, sigma1)
mixMPHDest = mixMPHD(x, sigma1, ini = ini)