On the geometric behaviour of multidimensional location measures |
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| Institution: | 1. Departamento de Matemáticas, Estadistica y Computación, Universidad de Cantabria, Arda. De Los Castros sln, 39071 Santander, Spain;2. Departamento de Estadística, Universidad de Valladolid, Spain;1. MOE Key Lab for Liquid-Solid Structure Evolution and Materials Processing, Institute of Materials Joining, Shandong University, Jinan 250061, China;2. Shandong Special Equipment Inspection Institute Co., Ltd., Jinan 250014, China |
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| Abstract: | We consider several generic geometric properties of location measures in the multivariate setting. Our study addresses the representativity of location measures by considering possible generalizations of the so-called Cauchy mean value property in a general framework mainly based on Φ-means.Our study shows that some caution is needed when using intuitive arguments because the mean is, in some sense, the only “intuitively well-behaved” multivariate location measure. |
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