Stochastic comparison for elliptically contoured random fields
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Lu, T., Du, J., & Ma, C. (2022). Stochastic comparison for elliptically contoured random fields. Statistics & Probability Letters, 189, 109594. https://doi.org/https://doi.org/10.1016/j.spl.2022.109594
This paper presents necessary and sufficient conditions for the peakedness comparison and convex ordering between two elliptically contoured random fields about their centers. A somewhat surprising finding is that the peakedness comparison for the infinite dimensional case differs from the finite dimensional case. For example, a Student’s t distribution is known to be more heavy-tailed than a normal distribution, but a Student’s t random field and a Gaussian random field are not comparable in terms of the peakedness. In particular, the peakedness comparison and convex ordering are made for isotropic elliptically contoured random fields on compact two-point homogeneous spaces.
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