Testing Empty Intersection between the Expected Value of a Random Interval and a Given Interval
Ana Belén Ramos-Guajardo¹, Gil González-Rodríguez², Ana Colubi², María Άngeles Gil²
¹Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing, Mieres, Asturias, Spain; ²Statistics, Operational Research and Mathematic Didactics, University of Oviedo, Oviedo, Asturias, Spain

The problem of testing the inclusion of the expected value of a normal random variable in a fixed interval has been studied in the literature as a multiple hypothesis test (see [4]). In previous works this test has been extended to the context in which random intervals are involved (see [3]). However there exist other situations in which the aim is centered on analyzing if the mean of a random interval and a given interval are disjoint or not. For instance this is the case of the mean of the perceptions provided by the experts about the quality of a specific product and an interval previously fixed which represents bad quality. Thus, in this work a hypothesis test to analyze if the expected value of a random interval and another interval have empty intersection is presented by using asymptotic and bootstrap techniques. Both approaches have been useful in the hypothesis testing context when imprecise values are considered (see, for instance, [1,2]). Finally, some simulations are carried out to show the empirical behaviour of the test and the method has been applied in a real-life situation.

[1] González-Rodríguez, G., Montenegro, M., Colubi, A. & Gil, M.A. (2006). Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data. Fuzzy Sets and Systems, 157, 2608-2613.

[2] Montenegro, M., Colubi, A., Casals, M.R. & Gil, M.A. (2004). Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika, 59, 31-49.

[3] Ramos-Guajardo, A.B., González-Rodríguez, G., Gil, M.A. (2010). Inclusion test of the expected value of a random interval in a given interval. In: Abstracts of 4th CSDA International Conference on Computational and Financial Econometrics and 3rd International Conference of the ERCIM Working Group on Computing & Statistics (CFE 10 & ERCIM 10, Senate House, University of London, UK), 50.

[4] Roy, S.N. (1953). On a heuristic method of test construction and its use in multivariate analysis. Annals of Mathematical Statistics, 24 (2), 220-238.

Keywords: Inclusion test; Expected value; Empty intersection; Asymptotic and bootstrap techniques

Biography: I'm working since November, 2007, in the Unit of Intelligent Data Analysis and Graphical Models of the European Centre for Soft Computing, in Mieres, Asturias, Spain as a research assistant.