Statistical estimation of a mixture of Gaussian distributions

Rudzkis, Rimantas; Radavičius, Marijus

doi:10.1007/bf00992613

Cited by 13 publications

(12 citation statements)

References 22 publications

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“…The resulting estimate with the highest likelihood function L(θ) is taken. The sequential mixture components extraction method described in [7,27,31] could be used here as well.…”

Section: Sample Clustering With the Em Algorithmmentioning

confidence: 99%

Accuracy of Nonparametric Density Estimation for Univariate Gaussian Mixture Models: A Comparative Study

Arnastauskaitė

Ruzgas

2020

Mathematical Modelling and Analysis

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Flexible and reliable probability density estimation is fundamental in unsupervised learning and classification. Finite Gaussian mixture models are commonly used for this purpose. However, the parametric form of the distribution is not always known. In this case, non-parametric density estimation methods are used. Usually, these methods become computationally demanding as the number of components increases. In this paper, a comparative study of accuracy of some nonparametric density estimators is made by means of simulation. The following approaches have been considered: an adaptive bandwidth kernel estimator, a projection pursuit estimator, a logspline estimator, and a k-nearest neighbor estimator. It was concluded that data clustering as a pre-processing step improves the estimation of mixture densities. However, in case data does not have clearly defined clusters, the pre-preprocessing step does not give that much of advantage. The application of density estimators is illustrated using municipal solid waste data collected in Kaunas (Lithuania). The data distribution is similar (i.e., with kurtotic unimodal density) to the benchmark distribution introduced by Marron and Wand. Based on the homogeneity tests it can be concluded that distributions of the municipal solid waste fractions in Kutaisi (Georgia), Saint-Petersburg (Russia), and Boryspil (Ukraine) are statistically indifferent compared to the distribution of waste fractions in Kaunas. The distribution of waste data collected in Kaunas (Lithuania) follows the general observations introduced by Marron and Wand (i.e., has one mode and certain kurtosis).

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“…The resulting estimate with the highest likelihood function L(θ) is taken. The sequential mixture components extraction method described in [7,27,31] could be used here as well.…”

Section: Sample Clustering With the Em Algorithmmentioning

confidence: 99%

Accuracy of Nonparametric Density Estimation for Univariate Gaussian Mixture Models: A Comparative Study

Arnastauskaitė

Ruzgas

2020

Mathematical Modelling and Analysis

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“…The result with the maximal value of L( θ) is selected as final. The methodology of consecutive extraction of the mixture components [11] can be also applied.…”

Section: Sample Clustering Using the Em Algorithmmentioning

confidence: 99%

Clustering Effect on the Statistical Estimation Accuracy of Distribution Density

Rudzkis¹,

Ruzgas²

2007

Acta Appl Math

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The paper is devoted to statistical nonparametric estimation of multivariate distribution density. The influence of data pre-clustering on the estimation accuracy of multimodal density is analyzed by means of the Monte Carlo method. It is shown that the soft clustering is more advantageous than the hard one. While a moderate increase in the number of clusters also increases the calculation time, it considerably reduces the estimation error.

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“…Fh+uj # Fh * ~oi" (9) For the proof of the theorems stated above the following two lemmas, possessing also the independent interest, are used. Let (6), (13) (6) is replaced by the weaker condition…”

Section: K} and Some H = H(j) E {Vl Vt} We Havementioning

confidence: 99%

“…Then Jr(-) is completely defined by the parameters Pi, Mi, Ri, i = 1 ..... q; however, to estimate them, especially when the dimensionality of X is large, is a highly complicated task (see, e.g. [9]). In practice, however, one rather frequently meets a situation where distributions of a part of components of the rvc's Yi coincide, or in a more general formulation, where a linear projection of the observations onto a space of less dimensionality (we will call it a discriminant space (DS)) preserves all statistical information about the a posteriori prababilities re(.…”

Section: Introductionmentioning

confidence: 99%

Mixtures of Gaussian distributions and projection pursuit preserving information about cluster structure

Rudzkis¹,

Radavičius²

1997

Lith Math J

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Statistical estimation of a mixture of Gaussian distributions

Cited by 13 publications

References 22 publications

Accuracy of Nonparametric Density Estimation for Univariate Gaussian Mixture Models: A Comparative Study

Accuracy of Nonparametric Density Estimation for Univariate Gaussian Mixture Models: A Comparative Study

Clustering Effect on the Statistical Estimation Accuracy of Distribution Density

Mixtures of Gaussian distributions and projection pursuit preserving information about cluster structure

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