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Added by
Jon A. Wellner
Publication date
2010
fields
Mathematical Statistics
and research's language is
English
Authors
Fuchang Gao
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A bracketing metric entropy bound for the class of Laplace transforms of probability measures on [0,infty) is obtained through its connection with the small deviation probability of a smooth Gaussian process. Our results for the particular smooth Gaussian process seem to be of independent interest.
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We give upper and lower bounds on the number of delta-matroids, and on the number of even delta-matroids.
In this paper we propose a class of weighted rank correlation coefficients extending the Spearmans rho. The proposed class constructed by giving suitable weights to the distance between two sets of ranks to place more emphasis on items having low rankings than those have high rankings or vice versa. The asymptotic distribution of the proposed measures and properties of the parameters estimated by them are studied through the associated copula. A simulation study is performed to compare the performance of the proposed statistics for testing independence using asymptotic relative efficiency calculations.
The median probability model (MPM) Barbieri and Berger (2004) is defined as the model consisting of those variables whose marginal posterior probability of inclusion is at least 0.5. The MPM rule yields the best single model for prediction in orthogonal and nested correlated designs. This result was originally conceived under a specific class of priors, such as the point mass mixtures of non-informative and g-type priors. The MPM rule, however, has become so very popular that it is now being deployed for a wider variety of priors and under correlated designs, where the properties of MPM are not yet completely understood. The main thrust of this work is to shed light on properties of MPM in these contexts by (a) characterizing situations when MPM is still safe under correlated designs, (b) providing significant generalizations of MPM to a broader class of priors (such as continuous spike-and-slab priors). We also provide new supporting evidence for the suitability of g-priors, as opposed to independent product priors, using new predictive matching arguments. Furthermore, we emphasize the importance of prior model probabilities and highlight the merits of non-uniform prior probability assignments using the notion of model aggregates.
We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gauge components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions of the nucleon spin. It is crucialy important to recognize the fact that the standard gauge fixing procedure is essentially a process of projecting out the physical components of the massless gauge field. A complexity of the nonabelian gauge theory as compared with the abelian case is that a closed expression for the physical component can be given only with use of the non-local Wilson line, which is generally path-dependent. It is known that, by choosing an infinitely long straight-line path in space and time, the direction of which is characterized by a constant 4-vector $n^mu$, one can cover a class of gauge called the general axial gauge, containing three popular gauges, i.e. the temporal, the light-cone, and the spatial axial gauge. Within this general axial gauge, we have calculated the 1-loop evolution matrix for the quark and gluon longitudinal spins in the nucleon. We found that the final answer is exactly the same independently of the choices of $n^mu$, which amounts to proving the gauge-independence and path-independence simultaneously, although within a restricted class of gauges and paths. By drawing on all of these findings together with well-established knowledge from gauge theories, we argue against the rapidly spreading view in the community that there are infinitely many decompositions of the nucleon spin.
We argue against the rapidly spreading idea of gauge-invariant-extension (GIE) approach in the nucleon spin decomposition problem, which implies the existence of infinitely many gauge-invariant decomposition of the nucleon spin.
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