Bootstrap approach to the multi-sample test of means with imprecise data

Gil, María Ángeles; Montenegro, Manuel; González‐Rodríguez, Gil; Colubi, Ana; Casals, María Rosa

doi:10.1016/j.csda.2006.04.018

Cited by 94 publications

(54 citation statements)

References 24 publications

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“…The covariance of two random fuzzy numbers can be also introduced (see González-Rodríguez et al [13], Blanco-Fernández et al [2]) in connection with the simple linear regression analysis between random fuzzy sets, although in this case it does not involve D Another statistical problem involving Bertoluzza et al's metric is that of testing about the population fuzzy-valued Aumann-type mean of one or more random fuzzy numbers on the basis of a sample of independent observations from it or them. More concretely (see Körner [20], Montenegro et al [25,26], González-Rodríguez et al [16,15], Gil et al [10], and Blanco-Fernández et al [2] …”

Section: Definition 3 Given a Probability Space (ω A P ) A Random mentioning

confidence: 99%

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Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Casals

Corral

Gil

et al. 2013

METRON

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Since Bertoluzza et al. 's metric between fuzzy numbers has been introduced, several studies involving it have been developed. Some of these studies concern equivalent expressions for the metric which are useful for either theoretical, practical or simulation purposes. Other studies refer to the potentiality of Bertoluzza et al.'s metric to establish statistical methods for the analysis of fuzzy data. This paper shortly reviews such studies and examine part of the scientific impact of the metric.

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Section: Definition 3 Given a Probability Space (ω A P ) A Random mentioning

confidence: 99%

“…In particular, if W is associated with the uniform distribution on {0, 1}, then d W reduces to δ 2 . On the other hand, if W is associated with the uniform distribution on [0, 1], which will be denoted along the paper by ℓ, then [6,10]),…”

Section: Figmentioning

confidence: 99%

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Casals

Corral

Gil

et al. 2013

METRON

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“…The most important point in traditional ANOVA is a test about the significance of the difference among population means. This test permits the user to conclude whether the differences among the means of several populations are too deviated to be attributed to the sampling error or not [7]. The basic formulas of classical ANOVA model can be referred to any statistical book [1,10,19], but the classical ANOVA has been briefly reviewed in "Classical ANOVA" of this manuscript from [21].…”

Section: Introduction and Literature Review Anovamentioning

confidence: 99%

Analysis of variance in uncertain environments

Parchami

Nourbakhsh

Mashinchi

2017

Complex Intell. Syst.

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Testing one-way analysis of variance (ANOVA) is used for experimental data analysis in which there is a continuous response variable and a single independent classification variable. In this paper, we extend one-way ANOVA to a case where observed data are imprecise numbers rather than real numbers. Several fast computable formulas are calculated for symmetric triangular and normal fuzzy data. Similar to the classical testing ANOVA, the total observed variation in the response variable is explained as the sum of observed variation due to the effects of the classification variable and the observed variation due to random error. A real case is given to clarify the proposed method.

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“…On the other hand, they approached large sample tests for simple fuzzy random variables. A bootstrap approach to ANOVA for fuzzy valued sample data is introduced in Gil et al [6] and Montenegro et al [7]. Lubiano and Trutschnig [8] used the R package SAFD (Statistical Analysis of Fuzzy Data).…”

Section: Introductionmentioning

confidence: 99%

Analysis of Variance for Fuzzy Data Based on Permutation Method

Lee

Jung

Lee

et al. 2017

IJFIS

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This paper deals with analysis of variance with fuzzy data (ANOVAF) based on permutation method. The permutation method is a nonparametric method introduced by Heap and Johnson for the data when the normal distribution cannot be assumed. We proposed two different approaches to test hypothesis of fuzzy means using the empirical distribution. To compare the results, several distances are considered especially using ρ-distance. Applying Monte Carlo simulation, it is confirmed through the numerical examples that the significant probability (p-value) get approached true parameter (p-value) regardless of distances or testing method based on proposed method. In addition, the number of permutation samples required is determined in the example to satisfy specified given accuracy.

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Bootstrap approach to the multi-sample test of means with imprecise data

Cited by 94 publications

References 24 publications

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Analysis of variance in uncertain environments

Analysis of Variance for Fuzzy Data Based on Permutation Method

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