Moderate Deviations for Degenerate U-processes
نویسنده
چکیده
Su cient conditions for a rank-dependent moderate deviations principle (MDP) for degenerate U -processes are presented. The MDP for VC classes of functions is obtained under exponential moments of the envelope. Among other techniques, randomization, decoupling inequalities and integrability of Gaussian and Rademacher chaos are used to present new Bernstein-type inequalities for U -processes which are the basis of our proofs of the MDP. We present a complete rank-dependent picture. The advantage of our approach is that we obtain in the degenerate case moderate deviations in non-Gaussian situations. c © 2000 Elsevier Science B.V. All rights reserved. MSC: 60F10 (primary); 60B12; 60G17
منابع مشابه
Moderate Deviations for Functional U-processes
The moderate deviations principle is shown for the partial sums processes built on U-empirical measures of Polish space valued random variables and on U-statistics of real valued kernel functions. It is proved that in the non-degenerate case the conditions for the time xed principles suuce for the moderate deviations principle to carry over to the corresponding partial sums processes. Given a u...
متن کاملRank-dependent Moderate Deviations of U-empirical Measures in Strong Topologies∗
We prove a rank-dependent moderate deviation principle for Uempirical measures, where the underlying i. i. d. random variables take values in a measurable (not necessarily Polish) space (S,S). The result can be formulated on a suitable subset of all signed measures on (Sm,S⊗m). We endow this space with a topology, which is stronger than the usual τ -topology. A moderate deviation principle for ...
متن کاملCramér Type Moderate Deviations for Studentized U-statistics
The U-statistic elegantly and usefully generalizes the notion of a sample mean. Typical examples include (i) sample mean: h(x1, x2) = 12 (x1 + x2); (ii) sample variance: h(x1, x2) = 12 (x1 − x2); (iii) Gini’s mean difference: h(x1, x2) = |x1 − x2|; (iv) one-sample Wilcoxon’s statistic: h(x1, x2) = 1(x1 + x2 ≤ 0). The non-degenerate U-statistic shares many limiting properties with the sample mea...
متن کاملModerate Deviations in a Random Graph and for the Spectrum of Bernoulli Random Matrices
We prove a moderate deviation principle for subgraph count statistics of ErdősRényi random graphs. This is equivalent in showing a moderate deviation principle for the trace of a power of a Bernoulli random matrix. It is done via an estimation of the logLaplace transform and the Gärtner-Ellis theorem. We obtain upper bounds on the upper tail probabilities of the number of occurrences of small s...
متن کاملA note on critical point and blow-up rates for singular and degenerate parabolic equations
In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000