CDF resampling for dataset expansion in Gaussian mixture models density estimation

This work presents a study on the short dataset performance of the goodness-of-fit density estimator previously presented by the authors. In case of complex densities, when the dataset does not contain enough samples for an accurate estimation of the underlying probability density function of the data, resampling techniques are used to expand the original sample set. In a novel approach that employs a goodness-of-fit measure to estimate the correct model order, the quality of the estimated mixture depends on the complexity of the true density and the length of the sample set. The poor performance experienced when estimating densities from short datasets can be corrected using a simple resampling of the empirical cumulative distribution, used to generate additional samples. When this technique is employed, the estimation quality is clearly improved and the resulting mixture better approximates the true density of the data.