A Wilcoxon-Mann-Whitney-type test for infinite-dimensional data

Chakraborty, Anirvan; Chaudhuri, Probal

doi:10.1093/biomet/asu072

Cited by 28 publications

(18 citation statements)

References 32 publications

(46 reference statements)

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“…The HDI and GI values were compared between the municipalities with and without CAs using the non-parametric Wilcoxon-Mann-Whitney test (CHAKRABORTY; CHAUDHURI, 2015;FAY;PROSCHAN, 2010). The municipalities with and without sustainable use CAs and those with and without full protection CAs were also compared separately.…”

Section: Methodsmentioning

confidence: 99%

Áreas De Conservação, Pobreza E Desigualdade Social: Avaliação Utilizando Indicadores Socioeconômicos Em Minas Gerais, Brasil

Salvio

Fontes

Silveira

et al. 2016

CERNE

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ABSTRACT:The objective of this study was to evaluate the possible correlations between the socioeconomic development indicators of the municipalities of Minas Gerais, Brazil, and the presence of both sustainable use and full protection conservation areas (CAs). The Human Development Index (HDI) and Gini Index (GI) values were compared between municipalities with and without CAs using the non-parametric Wilcoxon-MannWhitney test. The correlations between the HDI and GI of each municipality and its areas occupied by CAs were analyzed using the non-parametric Spearman correlation test. A total of 560 CAs were identified in the 853 municipalities of the state. The HDI values of municipalities with CAs were not significantly different from those of other areas, but significant differences were found in the GI values, which were higher in municipalities with CAs. No significant correlations were found between the HDI of municipalities and their areas occupied by CAs. However, significant correlations were found between the GI and areas occupied by CAs, suggesting that the CAs are associated with greater socioeconomic inequalities. Populations should be included in conservation efforts through programs that benefit these individuals, such as payment for environmental services and other conservation strategies. ÁREAS DE CONSERVAÇÃO, POBREZA E DESIGUALDADE SOCIAL: AVALIAÇÃO UTILIZANDO INDICADORES SOCIOECONÔMICOS EM MINAS GERAIS, BRASILRESUMO: Neste estudo objetivou-se avaliar as possíveis correlações entre os indicadores de desenvolvimento socioeconômico dos municípios do estado de Minas Gerais, Brasil, e a presença de unidades de conservação (UC), tanto de uso sustentável como de proteção integral. Os valores de Índice de Desenvolvimento Humano (IDH) e Índice de Gini (IG) foram comparados entre os municípios com e sem UC pelo teste não paramétrico Wilcoxon-Mann-Whitney. Testaram-se as correlações entre IDH e IG de cada município e suas áreas ocupadas por UC através do teste não paramétrico de correlação de Spearman. Identificaram-se 560 UC nos 853 municípios do estado. Os municípios com UC não apresentaram IDH significativamente diferentes dos demais, mas encontraramse diferenças significativas nos valores de IG, superiores nos municípios com UC. Não se encontraram correlações significativas entre os IDH dos municípios e suas áreas ocupadas por UC. Mas encontraram-se correlações significativas entre IG e as áreas ocupadas por UC, associando as UC a maiores desigualdades socioeconômicas. Deve-se incorporar as populações aos esforços de conservação por meio de programas que as beneficiem, em especial o pagamento por serviços ambientais, entre outras estratégias conservacionistas.

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Section: Methodsmentioning

confidence: 99%

Áreas De Conservação, Pobreza E Desigualdade Social: Avaliação Utilizando Indicadores Socioeconômicos Em Minas Gerais, Brasil

Salvio

Fontes

Silveira

et al. 2016

CERNE

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“…Further, it is shown in Oja (2010, pp. Recently, a two sample Wilcoxon-Mann-Whitney type test based on spatial ranks in infinite dimensional spaces has been studied by Chakraborty and Chaudhuri (2015). In any separable Banach space, the asymptotic distributions of T SR and Q T SR are the same.…”

Section: Definition 201mentioning

confidence: 99%

Modern Nonparametric, Robust and Multivariate Methods

Nordhausen¹,

Taskinen²

2015

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“…(2) 0 for large values of ||T SR ||. Recently, a two sample Wilcoxon-Mann-Whitney type test based on spatial ranks in infinite dimensional spaces have been studied by Chakraborty and Chaudhuri (2014). Note that if X = R, S x = sign(x).…”

Section: We Reject Hmentioning

confidence: 99%

Paired Sample Tests in Infinite Dimensional Spaces

Chakraborty

Chaudhuri

2015

Modern Nonparametric, Robust and Multivariate Methods

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The sign and the signed-rank tests for univariate data are perhaps the most popular nonparametric competitors of the t test for paired sample problems. These tests have been extended in various ways for multivariate data in finite dimensional spaces. These extensions include tests based on spatial signs and signed ranks, which have been studied extensively by Hannu Oja and his coauthors. They showed that these tests are asymptotically more powerful than Hotelling's T 2 test under several heavy tailed distributions. In this paper, we consider paired sample tests for data in infinite dimensional spaces based on notions of spatial sign and spatial signed rank in such spaces. We derive their asymptotic distributions under the null hypothesis and under sequences of shrinking location shift alternatives. We compare these tests with some mean based tests for infinite dimensional paired sample data. We show that for shrinking location shift alternatives, the proposed tests are asymptotically more powerful than the mean based tests for some heavy tailed distributions and even for some Gaussian distributions in infinite dimensional spaces. We also investigate the performance of different tests using some simulated data.

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A Wilcoxon-Mann-Whitney-type test for infinite-dimensional data

Cited by 28 publications

References 32 publications

Áreas De Conservação, Pobreza E Desigualdade Social: Avaliação Utilizando Indicadores Socioeconômicos Em Minas Gerais, Brasil

Áreas De Conservação, Pobreza E Desigualdade Social: Avaliação Utilizando Indicadores Socioeconômicos Em Minas Gerais, Brasil

Modern Nonparametric, Robust and Multivariate Methods

Paired Sample Tests in Infinite Dimensional Spaces

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