1,721,001 research outputs found
On the behavior of the conditional expectations in Skorohod representation theorem
No full textIn this paper we deal with the Skorohod representation of a given system of probability measures. More precisely, we give conditions for the existence of a Skorohod representation (X,(Xn)) with the following additional property: for each real number p⩾1 and each real random variable Z in Lp, the conditional expectation E[Z|Xn] converges in Lp to the conditional expectation E[Z|X
A dose-finding sequential method for targeting a given mean response: Up&Down experiments
No full textTradizionalmente, gli studi dose-risposta sono esperimenti di tipo binario volti a stimare un determinato “quantile” di interesse di una curva di risposta. In questo lavoro si considera il caso in cui la risposta osservata sia una generica variabile aleatoria reale, non necessariamente dicotomica, e lo scopo dell’esperimento consiste nello stimare la dose target associata ad una preassegnata risposta media. Ripercorrendo i risultati di Giovagnoli e Pintacuda (1998) e Baldi Antognini et al (2006), viene proposta ed analizzata un’estensione randomizzata dell’algoritmo up-and-down, fornendo inoltre una
procedura di stima della risposta media basata sul metodo di massima verosimiglianza
Central limit theorems for an Indian buffet model with random weights
No full textThe three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let be the number of dishes experimented by the first customers, and let where is the number of dishes tried by customer . The asymptotic distributions of and , suitably centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., non generalized) Indian buffet process
Asymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan Variance
Full text linkIn order to estimate the memory parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with other methods. In this paper we present a rigorous study of the MAVAR log-regression estimator. In particular, under the assumption that the signal process is a fractional Brownian motion, we prove that it is consistent and asymptotically normally distributed. Finally, we discuss its connection with the wavelets estimators
Interacting nonlinear reinforced stochastic processes: Synchronization or non-synchronization
No full textThe rich-get-richer rule reinforces actions that have been frequently chosen in the past. What happens to the evolution of individuals’ inclinations to choose an action when agents interact? Interaction tends to homogenize, while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes have recently been considered in many papers, in which the asymptotic behavior is proven to exhibit almost sure synchronization. In this paper we consider models where, even if interaction among agents is present, absence of synchronization may happen because of the choice of an individual nonlinear reinforcement. We show how these systems can naturally be considered as models for coordination games or technological or opinion dynamics
Central limit theorems for an Indian buffet model with random weights
No full textThe three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let Ln be the number of dishes experimented by the first n customers, and let K ̄ ̄ ̄ ̄ ̄n=(1/n)∑ni=1Ki where Ki is the number of dishes tried by customer i. The asymptotic distributions of Ln and K ̄ ̄ ̄ ̄ ̄n, suitably centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., nongeneralized) Indian buffet process
Statistical test for an urn model with random multidrawing and random addition
No full textWe complete the study of the model introduced in Crimaldi et al., (2022). It is a two-color urn model with multiple drawing and random (non-balanced) time-dependent reinforcement matrix. The number of sampled balls at each time-step is random. We identify the exact rates at which the number of balls of each color grows to +infinity and define two strongly consistent estimators for the limiting reinforcement averages. Then we prove a Central Limit Theorem, which allows to design a statistical test for such averages.(c) 2023 Elsevier B.V. All rights reserved
A generalized telegraph process with velocity driven by random trials
No full textWe consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates. © Applied Probability Trust 2013
Weighted networks as randomly reinforced urn processes
No full textWe analyze weighted networks as randomly reinforced urn processes, in which the edge-total weights are determined by a reinforcement mechanism. We develop a statistical test and a procedure based on it to study the evolution of networks over time, detecting the "dominance" of some edges with respect to the others and then assessing if a given instance of the network is taken at its steady state or not. Distance from the steady state can be considered as a measure of the relevance of the observed properties of the network. Our results are quite general, in the sense that they are not based on a particular probability distribution or functional form of the random weights. Moreover, the proposed tool can be applied also to dense networks, which have received little attention by the network community so far, since they are often problematic. We apply our procedure in the context of the International Trade Network, determining a core of "dominant edges." © 2013 American Physical Society
Analysis of a Hurst parameter estimator based on the modified Allan variance
No full textIn order to estimate the Hurst parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with an other method of common use based on wavelet analysis. Here we link it to the wavelets setting and stress why a different analysis for the two approaches is required. We then focus on the asymptotic analysis of the MAVAR log-regression estimator and provide new formulas for the related confidence intervals. By numerical evaluation, we analyze these formulas and make a comparison between three suitable choices on the regression weights, also optimizing over different choices on the data progression
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