Inclusion degree tests for the Aumann expectation of a random interval

Ramos-Guajardo, Ana Belén; Colubi, Ana; González‐Rodríguez, Gil

doi:10.1016/j.ins.2014.08.013

Cited by 14 publications

(12 citation statements)

References 24 publications

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“…Of course, each further activity based on (25) requires a prior settlement on the relative importance between the difference in location and spread expressed by γ. Quite a different approach was suggested by Ramos-Guajardo et al 28,32,33 who proposed a test for a hypothesis about a similarity between the expected value of a random interval and a fixed interval. In both cases, the crucial difficulty is to find the distribution of the test statistic, so the advised way-out is to use a bootstrap or to apply an asymptotic approach, provided a sample is large enough.…”

Section: Random Intervalmentioning

confidence: 99%

“…3,4 Interval-valued data that appear in different contexts drew the attention of many researchers. Various problems concerning interval-valued data in regression analysis, [5][6][7][8][9] time series, 10 principal component analysis, 11,12 correlation analysis, 13,14 classification, 9,[15][16][17][18][19][20][21] clustering, 22,23 analysis of variance, 24 and hypothesis testing [25][26][27][28][29][30][31][32][33] have been deeply studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The sign test and the signed‐rank test for interval‐valued data

Grzegorzewski

Śpiewak

2019

Int J Intell Syst

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Two versions of the generalized sign test and the signed‐rank test for interval‐valued data (both for one‐sample and paired two‐sample problem) are proposed. These two versions correspond to different possible views on the interval outcomes of the experiment—either the epistemic or the ontic one. Each view yields its own approach to data analysis which results in different test construction and the way of carrying on the statistical inference.

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Section: Random Intervalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The sign test and the signed‐rank test for interval‐valued data

Grzegorzewski

Śpiewak

2019

Int J Intell Syst

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“…In addition, the similarity measure in (5) can be also viewed as a kind of inclusion degree of A in B (see [8,13]). Some hypothesis tests for checking the inclusion degree of the expectation of an interval in a previously pre-fixed interval have been developed in [11]. Specifically, the two sided-test for the expected value of a random interval is a particular case of the test in [11] when the inclusion degree equals 1.…”

Section: Interval Data and One-sided Hypothesesmentioning

confidence: 99%

“…Some hypothesis tests for checking the inclusion degree of the expectation of an interval in a previously pre-fixed interval have been developed in [11]. Specifically, the two sided-test for the expected value of a random interval is a particular case of the test in [11] when the inclusion degree equals 1. Thus, the corresponding one-side tests can be easily addressed taking into account an analogous procedure as we will show below.…”

Section: Interval Data and One-sided Hypothesesmentioning

confidence: 99%

Similarity based one-sided tests for the expected value and interval data

Grzegorzewski¹,

Ramos-Guajardo²

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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A novel way for addressing one-sided hypothesis tests for the mean of unable to observe real random variables from which we have information provided in terms of interval data is proposed. For this purpose, a measure of similarity between intervals is considered and the classical one-sided hypothesis test to check whether the similarity between the expectation of a random interval and a subset of an specific unbounded interval is high enough. Asymptotic and bootstrap techniques are applied in order to study the limit distribution of the proposed test statistic. Some simulations have been carried out in order to show the empirical behavior of the test.

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“…One option to slacken the strict equality is to consider a measure of inclusion. In this context, one-sample inclusion tests for the Aumann expectation of RIs have been addressed in [22] leading to the proposal of one-sided tests as a particular case in spite of the lack of order between interval data. The inclusion measure considered in that work was introduced by Sánchez [26] and is defined as a ratio between the measure of the intersection of two intervals (introduced in [27]) and the measure of the reference interval.…”

Section: Introductionmentioning

confidence: 99%

Testing the degree of overlap for the expected value of random intervals

Ramos-Guajardo

González‐Rodríguez

Colubi

2020

International Journal of Approximate Reasoning

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Some hypothesis tests for analyzing the degree of overlap between the expected value of random intervals are provided. For this purpose, a suitable measure to quantify the overlapping grade between intervals is considered on the basis of the Szymkiewicz-Simpson coefficient defined for general sets. It can be seen as a kind of likeness index to measure the mutual information between two intervals. On one hand, an estimator for the proposed degree of overlap between intervals is provided and its strong consistency is analyzed. On the other hand, two tests are also proposed in this framework: a one-sample test to examine the degree of overlap between the expected value of a random interval and a given interval, and a two-sample test to check the degree of overlap between the expected value of two random intervals. To solve such hypothesis tests, two statistics are suggested and their limit distributions are studied by considering both asymptotic and bootstrap techniques. Their power has been also explored by means of local alternatives. In addition, some simulation studies are carried out to investigate the behavior of the proposed approaches. Finally, the performance of the tests is also reported in a real-life application.

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Inclusion degree tests for the Aumann expectation of a random interval

Cited by 14 publications

References 24 publications

The sign test and the signed‐rank test for interval‐valued data

The sign test and the signed‐rank test for interval‐valued data

Similarity based one-sided tests for the expected value and interval data

Testing the degree of overlap for the expected value of random intervals

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