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

Abstract

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.

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

“…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.…”

“…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.…”

Flexible bootstrap based on the canonical representation of fuzzy numbers

“…Summing up the forementioned considerations and (11), (12) and (13), we obtain the following bootstrap algorithm for trapezoidal fuzzy data Algorithm 2.…”

“…Nowadays, statistical tests for fuzzy sample attract attention of many researches (see, e.g., [8,10,12,15,17,20]). Most of these tests utilize bootstrap methods to determine a null distribution under study.…”

“…Hence, in fuzzy context the bootstrap appears as not only helpful but sometimes even the onliest tool that enables to conduct any statistical reasoning. In particular, the bootstrapped version of statistical tests for fuzzy data were considered, e.g., by Colubi et al [3], Gil et al [8], González-Rodríguez et al [9,10], Grzegorzewski and Ramos-Guajardo [12], Montenegro et al [17] and Ramos-Guajardo and Lubiano [20]. Some other examples on the bootstrap application in fuzzy modeling of the real-life problems, like fuzzy rating in questionnaires [16], quality control in cheese manufacturing [19] or fuzzy nonparametric Shewhart's control chart construction [23] are worth mentioning too.…”