The longitudinal regression model where is the th measurement of the th subject at random time , is the regression function, is a predictable covariate process observed at time and is a noise, is studied in marked point process framework. In this paper we introduce the assumptions which guarantee the consistency and asymptotic normality of smooth -estimator of unknown parameter .
Let , , where the are independent random vectors, each uniformly distributed on the unit sphere in ℝⁿ, and are real constants. We prove that if is majorized by in the sense of Hardy-Littlewood-Pólya, and if Φ: ℝⁿ → ℝ is continuous and bisubharmonic, then EΦ(X) ≤ EΦ(Y). Consequences include most of the known sharp Khinchin inequalities for sums of the form X. For radial Φ, bisubharmonicity is necessary as well as sufficient for the majorization inequality to always hold. Counterparts...
Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.