1,721,068 research outputs found
Asymptotic results for runs and empirical cumulative entropies.
Full text linkWe prove large and moderate deviations for two sequences of estimators based on the order statistics and, more precisely, on spacings. In the first case we deal with runs, and we have sums of independent Bernoulli distributed random variables. In the second case we deal with empirical cumulative entropies, and we have linear combinations of independent exponentially distributed random variables
Non-universal moderate deviation principle for the nodal length of arithmetic Random Waves
Full text linkInspired by the recent work Macci et al. (2021), we prove a non-universal non-central
Moderate Deviation Principle for the nodal length of arithmetic random waves (Gaussian Laplace
eigenfunctions on the standard flat torus) both on the whole manifold and on shrinking toral domains. Second order fluctuations for the latter were established by Marinucci et al. (2016) and
Benatar et al. (2020) respectively, by means of chaotic expansions, number theoretical estimates
and full correlation phenomena. Our proof is simple and relies on the interplay between the long
memory behavior of arithmetic random waves and the chaotic expansion of the nodal length, as well
as on well-known techniques in Large Deviation theory (the contraction principle and the concept
of exponential equivalence)
Asymptotic results for linear combinations of spacings generated by i.i.d. exponential random variables
No full textWe prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous functions defined on [0, 1] which satisfy some suitable conditions. In this way we generalize some recent results by Giuliano et al. (J Statist Plann Inference 157–158:77–89, 2015) which concern the empirical cumulative entropies defined in Di Crescenzo et al. (J Statist Plann Inference 139:4072–4087, 2009a)
An inverse Sanov theorem for exponential families
Full text linkWe prove the large deviation principle (LDP) for posterior distributions
arising from subfamilies of full exponential families, allowing
misspecification of the model. Moreover, motivated by the so-called inverse
Sanov Theorem (see e.g. Ganesh and O'Connell 1999 and 2000), we prove the LDP
for the corresponding maximum likelihood estimator, and we study the
relationship between rate functions. In our setting, even in the non
misspecified case, it is not true in general that the rate functions for
posterior distributions and for maximum likelihood estimators are
Kullback-Leibler divergences with exchanged arguments
Noncentral moderate deviations for time-changed Lévy processes with inverse of stable subordinators
No full textThis paper presents some extensions of recent noncentral moderate deviation results. In the first part, the results in [Statist. Probab. Lett. 185, Paper No. 109424, 8 pp. (2022)] are generalized by considering a general Lévy process instead of a compound Poisson process. In the second part, it is assumed that has bounded variation and is not a subordinator; thus can be seen as the difference of two independent nonnull subordinators. In this way, the results in [Mod. Stoch. Theory Appl. 11, 43–61] for Skellam processes are generalized
Asymptotic results for a multivariate version of the alternative fractional Poisson process
No full textA multivariate fractional Poisson process was recently defined in
Beghin and Macci (2016) by considering a common independent random
time change for a finite dimensional vector of independent
(non-fractional) Poisson processes; moreover it was proved that
it has suitable multinomial conditional distributions of the
components given their sum. In this paper we consider another
multivariate process with the same conditional distributions of the
components given their sums, and different marginal distributions
of the sums; more precisely we assume that the one-dimensional
marginal distributions of the sum-process coincide with the ones of
the alternative fractional (univariate) Poisson process in Beghin
and Macci (2013). We present large deviation results, and this
generalizes the result in Beghin and Macci (2013) concerning the
univariate case. We also study moderate deviations and we present
some statistical applications concerning the estimation of the
fractional parameter
Asymptotic results for weighted means of random variables which converge to a Dickman distribution, and some number theoretical applications
Full text linkThis paper studies some examples of weighted means of random variables. These weighted means generalize the logarithmic means. We consider different kinds of random variables and
we prove that they converge weakly to a Dickman distribution; this extends some known results in the literature. In some cases we have interesting connections with number theory. Moreover
we prove large deviation principles and, arguing as in [16], we illustrate how the rate function can be expressed in terms of the Hellinger distance with respect to the (weak) limit, i.e. the
Dickman distribution
Large deviations for method-of-quantiles estimators of one-dimensional parameters
No full textWe consider method-of-quantiles estimators of unknown one-dimensional parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level λ∈(0,1). The aim is to present large deviation results for these estimators as the sample size tends to infinity. We study in detail several examples; for specific models we discuss the choice of the optimal value of λ and we compare the convergence of the method-of-quantiles and method-of-moments estimators
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