mixLogconcHD function

Clustering with Mixtures of Log-concave Distributions using EM Algorithm (Multivariate)

`mixLogconcHD' is used to estimate the parameters of a mixture of multivariate log-concave distributions. The correlation structure among components is calculated by the normal copula.

mixLogconcHD(x, C, ini = NULL, nstart = 20, tol = 1e-05, maxiter = 100)

Arguments

• x: an n by p data matrix where n is the number of observations and p is the dimension of the data.
• C: number of mixture components.
• ini: initial value for the EM algorithm. Default value is NULL, which obtains the initial value using the EMnormal function. It can be a list with the form of list(pi, mu, sigma), where pi is a 1 by C matrix of mixing proportions, mu is a C by p matrix of component means, and sigma is a p by p by C array of standard deviations or covariance matrices of C mixture components.
• nstart: number of initializations to try. Default is 20.
• tol: stopping criteria (threshold value) for the EM algorithm. Default is 1e-05.
• maxiter: maximum number of iterations for the EM algorithm. Default is 100.

Returns

A list containing the following elements: - loglik: final log-likelihood.

• pi: estimated mixing proportions.

• f: component densities at x.

• sigma: estimated standard deviation or covariance matrix.

Examples

x = mvtnorm::rmvnorm(100, c(0, 0), matrix(c(2, 1, 1, 2), nrow = 2))
x = matrix(x, nrow = 100)
x[1:60, ] = x[1:60, ] + 5
EMlogc = mixLogconcHD(x, C = 2)

References

Chang, G. T., and Walther, G. (2007). Clustering with mixtures of log-concave distributions. Computational Statistics & Data Analysis, 51(12), 6242-6251.

Hu, H., Wu, Y., and Yao, W. (2016). Maximum likelihood estimation of the mixture of log-concave densities. Computational Statistics & Data Analysis, 101, 137-147.

See Also

mixLogconc