Multivariate goodness-of-fit tests based on kernel density estimators

Bakshaev, Aleksej; Rudzkis, Rimantas

doi:10.15388/na.2015.4.9

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…For that, we would require an Ndimensional two-sample test. However, in contrast to the univariate case, the probability distribution functions of statistics Kolmogorov-Smirnov and Anderson-Darling in the multivariate case are not distribution-free [24]. Bakšajev and Rudzkis note that this problem can be overcome by using the Rosenblatt transformation, as shown in [25].…”

Section: Statistical Distancesmentioning

confidence: 99%

See 1 more Smart Citation

Hierarchical Qualitative Clustering: clustering mixed datasets with critical qualitative information

Seca,

Mendes-Moreira,

Mendes-Neves

et al. 2020

Preprint

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Clustering can be used to extract insights from data or to verify some of the assumptions held by the domain experts, namely data segmentation. In the literature, few methods can be applied in clustering qualitative values using the context associated with other variables present in the data, without losing interpretability. Moreover, the metrics for calculating dissimilarity between qualitative values often scale poorly for high dimensional mixed datasets. In this study, we propose a novel method for clustering qualitative values, based on Hierarchical Clustering (HQC), and using Maximum Mean Discrepancy. HQC maintains the original interpretability of the qualitative information present in the dataset. We apply HQC to two datasets. Using a mixed dataset provided by Spotify, we showcase how our method can be used for clustering music artists based on the quantitative features of thousands of songs. In addition, using financial features of companies, we cluster company industries, and discuss the implications in investment portfolios diversification.

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Section: Statistical Distancesmentioning

confidence: 99%

“…Bakšajev and Rudzkis note that this problem can be overcome by using the Rosenblatt transformation, as shown in [25]. However, the same authors also note considerable difficulties in computing the statistical distances mentioned using this process [24].…”

Section: Statistical Distancesmentioning

confidence: 99%

Hierarchical Qualitative Clustering: clustering mixed datasets with critical qualitative information

Seca,

Mendes-Moreira,

Mendes-Neves

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Among them, distances between densities (after kernel smoothing) have attracted much interest, starting with Bickel and Rosenblatt (1973) in the univariate case. Bakshaev and Rudzkis (2015) recently proposed a multivariate extension; the choice of a bandwidth matrix, however, dramatically affects the outcome of the resulting testing procedure. Fan (1997) considers a distance between characteristic functions, which accommodates arbitrary dimensions; the idea is appealing but the estimation of the integrals involved in the distance seems tricky.…”

Section: Introductionmentioning

confidence: 99%

Multivariate goodness-of-fit tests based on Wasserstein distance

Hallin

Mordant²,

Segers³

2021

Electron. J. Statist.

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Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary reduction of the data via invariance. This property allows for calculation of exact critical values and p-values at finite sample sizes. Applications include testing for location-scale families and testing for families arising from affine transformations, such as elliptical distributions with given standard radial density and unspecified location vector and scatter matrix. A novel test for multivariate normality with unspecified mean vector and covariance matrix arises as a special case. For more general parametric families, we propose a parametric bootstrap procedure to calculate critical values. The lack of asymptotic distribution theory for the empirical Wasserstein distance means that the validity of the parametric bootstrap under the null hypothesis remains a conjecture. Nevertheless, we show that the test is consistent against fixed alternatives. To this end, we prove a uniform law of large numbers for the empirical distribution in Wasserstein distance, where the uniformity is over any class of underlying distributions satisfying a uniform integrability condition but no additional moment assumptions. The calculation of test statistics boils down to solving the well-studied semi-discrete optimal transport problem. Extensive numerical experiments demonstrate the practical feasibility and the excellent performance of the proposed tests for the Wasserstein distance of order p = 1 and p = 2 and for dimensions at least up to d = 5. The simulations also lend support to the conjecture of the asymptotic validity of the parametric bootstrap.

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Goodness-of-fit tests based on the empirical characteristic function

Bakshaev

Rudzkis

2017

Lith Math J

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Multivariate goodness-of-fit tests based on kernel density estimators

Cited by 3 publications

References 29 publications

Hierarchical Qualitative Clustering: clustering mixed datasets with critical qualitative information

Hierarchical Qualitative Clustering: clustering mixed datasets with critical qualitative information

Multivariate goodness-of-fit tests based on Wasserstein distance

Goodness-of-fit tests based on the empirical characteristic function

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