Rényi-type empirical processes
نویسندگان
چکیده
منابع مشابه
Explosive Percolation in Erdős-Rényi-Like Random Graph Processes
The evolution of the largest component has been studied intensely in a variety of random graph processes, starting in 1960 with the Erdős-Rényi process (ER). It is well known that this process undergoes a phase transition at n/2 edges when, asymptotically almost surely, a linear-sized component appears. Moreover, this phase transition is continuous, i.e., in the limit the function f(c) denoting...
متن کاملEmpirical Processes : Notes 1
See, for example, Billingsley (Prob. & Measure) for a proof. Donsker’s theorem deals with the convergence, in distribution, of the empirical process. In what follows I will assume the basic concepts of convergence in distribution for stochastic processes assuming values in a metric space. Billingsley’s book on weak convergence (especially the 2nd edition) is an excellent reference (in particula...
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over all (α, β). This gives us our standard least squares estimates (α̂, β̂), whose consistency we will take for granted in the ensuing discussion. Thus: (α̂, β̂) = argmin(α,β) Mn(α, β) . It is not difficult to check that: (α0, β0) = argmin(α,β)M(α, β) , where M(α, β) = P [(Y − α − β X)2] where P is the distribution of (X,Y ). Check that, up to a constant, M is a second order polynomial in (α, β) w...
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Shannon and Rényi information theory have been applied to coupling estimation in complex systems using time series of their dynamical states. By analysing how information is transferred between constituent parts of a complex system, it is possible to infer the coupling parameters of the system. To this end, we introduce the partial Rényi transfer entropy and we give an alternative derivation of...
متن کاملMartingale Property of Empirical Processes ¤
It is shown that for a large collection of almost independent martingales in a suitable framework, the martingale property is preserved on the empirical processes almost surely. Under the assumptions of almost independence and essentially identical finite dimensional distributions, it is proven that a large collection of stochastic processes are martingales essentially if and only if so are the...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1992
ISSN: 0047-259X
DOI: 10.1016/0047-259x(92)90073-o