mixTest function

Goodness of Fit Test for Finite Mixture Models

`mixTest' is used to perform a goodness-of-fit test for finite mixture models (Wichitchan et al., 2019). It returns five types of goodness-of-fit statistics and determines the number of components in the mixture model based on the Kolmogorov-Smirnov (KS) statistic. The test is performed using bootstrapping.

mixTest(x, alpha = 0.10, C.max = 10, nboot = 500, nstart = 5)

Arguments

• x: a vector of observations.
• alpha: significance level of the test.
• C.max: maximum number of mixture components considered in the test. The test is performed for 2 to C.max components.
• nboot: number of bootstrap resampling. Default is 500.
• nstart: number of initializations to try. Default if 5.

Returns

A list containing the following elements: - GOFstats: vector of test statistics calculated from data, in the order of c(ks, cvm, kui, wat, ad).

• ks: vector of the Kolmogorov-Smirnov (KS) statistic for each bootstrap sample.

• cvm: vector of the Cramer-Von Mises statistic for each bootstrap sample.

• kui: vector of the Kuiper's statistic for each bootstrap sample.

• wat: vector of the Watson statistic for each bootstrap sample.

• ad: vector of the Anderson Darling statistic for each bootstrap sample.

• result: vector of test results based on the KS statistic. If the kth element in the vector is 1, k-component mixture model is significant based on the KS statistic; If 0, otherwise. See examples for details.

Examples

n = 100
mu = c(-2.5, 0)
sd = c(0.8, 0.6)
n1 = rbinom(n, 1, 0.3)
x = c(rnorm(sum(n1), mu[1], sd[1]), rnorm(n - sum(n1), mu[2], sd[2]))

# The result shows that two-component mixture model is statistically significant based on the KS.
out = mixTest(x, alpha = 0.10, C.max = 10, nboot = 500, nstart = 5)

References

Wichitchan, S., Yao, W., and Yang, G. (2019). Hypothesis testing for finite mixture models. Computational Statistics & Data Analysis, 132, 180-189.