mixMPHD function

Semiparametric Mixture Model by Minimizing Profile Hellinger Distance

`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 [REMOVE_ME]$h(x;\boldsymbol{\theta},f) = \pi f(x-\mu_1)+(1-\pi)f(x-\mu_2), [REMOVE_ME_2]$

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.

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.

Returns

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.

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

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.

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)

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.