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Weak convergence for the row sums of a triangular array of empirical processes under bracketing conditions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS 1998年第2期73卷 195-231页

作者： Arcones, MA Univ Texas Dept Math Austin TX 78712 USA

We study the weak convergence for the row sums of a triangular array of empirical processes under bracketing conditions involving majorizing measures. As an application, we consider the weak convergence of stochastic processes of the form {(a(n)(-1)Sigma f(Xj,t)) - c(n)(t) : t is an element of T}, n greater than or equal to 1, where {X-j)(j=1)(infinity) is a sequence of i.i.d.r.v.s with values in the measurable space (S, Y), f(., t) : S --> R is a measurable function for each t is an element of T, {a(n)} is an arbitrary sequence of real numbers and c(n)(t) is a real number, for each t is an element of T and each n greater than or equal to 1. We also consider the weak convergence of processes of the form {Sigma(j=1)(n) f(j)(X-j,t) : t is an element of T}, n greater than or equal to 1, where {X-j}(j=1)(infinity) is a sequence of independent r.v.s with values in the measurable space (S-j, Y-j), and f(j)(., t) : S-j --> R is a measurable function for each t is an element of T. Instead of measuring the size of the brackets using the strong or weak L-p norm, we use a distance inherent to the process. We present applications to the weak convergence of stochastic processes satisfying certain Lipschitz conditions. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： empirical processes triangular arrays bracketing majorizing measures

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On the maxima of suprema of dependent Gaussian models

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QUEUEING SYSTEMS 2023年第1-2期105卷 99-128页

作者： Ji, Lanpeng Peng, Xiaofan Univ Leeds Sch Math Woodhouse Lane Leeds LS29JT England Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China

In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima. The obtained results not only have potential applications in estimating the delay of certain Gaussian fork-join queueing systems but also provide interesting insights to the extreme value theory for triangular arrays of random variables with row-wise dependence.

关键词： Extreme value Self-similarity Gaussian processes Fractional Brownian motion triangular arrays Pickands constant Piterbarg constant

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Conditional convergence to infinitely divisible distributions with finite variance

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2005年第5期115卷 737-768页

作者： Dedecker, J Louhichi, S Univ Paris 06 Lab Stat Theor & Appl F-75013 Paris France Univ Paris 11 Lab Probabil Stat & Modelisat F-91405 Orsay France

We obtain new conditions for partial sums of an array with stationary rows to converge to a mixture of infinitely divisible distributions with finite variance. More precisely, we show that these conditions are necessary and sufficient to obtain conditional convergence. If the underlying sigma-algebras are nested, conditional convergence implies stable convergence in the sense of Renyi. From this general result we derive new criteria expressed in terms of conditional expectations, which can be checked for many processes such as m-conditionally centered arrays or mixing arrays. When it is relevant, we establish the weak convergence of partial sum processes to a mixture of Levy processes in the space of cadlag functions equipped with Skorohod's topology. The cases of Wiener processes, Poisson processes and Bernoulli distributed variables are studied in detail. (c) 2005 Elsevier B.V. All rights reserved.

关键词： infinitely divisible distributions Levy processes stable convergence triangular arrays mixing processes

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PARALLEL VLSI ALGORITHM FOR STABLE INVERSION OF DENSE MATRICES

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IEE PROCEEDINGS-E COMPUTERS AND DIGITAL TECHNIQUES 1989年第6期136卷 575-580页

作者： ELAMAWY, A DHARMARAJAN, KR Department of Electrical and Computer Engineering Louisiana State University Baton Rouge USA

A fast, efficient, parallel algorithm for stable matrix inversion based on Givens plane rotations is described. The algorithm is implemented on VLSI systolic architecture that is capable of inverting anyn×nnonsingular dense matrix in 5nunits of time, including I/O time. The array architecture consists ofn2+nprocessing elements (PEs) arranged as a cascade of two triangular arrays of (n2+n)/2 PEs each. The parallel algorithm involves the following processes:QR-decomposition by the Givens rotations technique; inversion of the upper triangular matrixRand multiplication ofR−1byQ. All three components of the algorithm are maximally overlapped with no need for intermediate I/O or global communications. A novel technique for concurrently inverting distinct matrices on the same array has also been suggested. This technique, based on the use of two levels of pipelining, significantly improves the array throughput. The execution speed of the algorithm matches that of the fastest systolic implementation of matrix inversion using Gaussian elimination without pivoting (which is unstable in most cases) reported to date.

关键词： Computer architecture Microprocessor chips Microprocessors and microcomputers cascade execution speed VLSI systolic architecture stable matrix inversion multiplication matrix algebra QR-decomposition upper triangular matrix nonsingular dense matrix parallel algorithms pipelining parallel architectures array throughput microprocessor chips Computer vision and image processing techniques Linear algebra (numerical analysis) triangular arrays VLSI Givens plane rotations

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An Innovative Architecture of Full-Digital Microphone arrays Over A²B Network for Consumer Electronics

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IEEE TRANSACTIONS ON CONSUMER ELECTRONICS 2022年第3期68卷 200-208页

作者： Pinardi, D. Rocchi, N. Toscani, A. Binelli, M. Chiorboli, G. Farina, A. Cattani, L. Univ Parma Dept Engn & Architecture I-43125 Parma Italy ASK Ind SpA Res & Dev Dept I-42124 Reggio Emilia Italy

Microphone arrays of various sizes and shapes are currently employed in consumer electronics devices such as speakerphones, smart TVs, smartphones, and headphones. In this paper, a full-digital, planar microphone array is presented. It makes use of digital Micro Electro-Mechanical Systems (MEMS) microphones, connected through the Automotive Audio Bus (A(2)B). A clock propagation model for A(2)B networks, developed in a previous work, was employed to estimate the effects of jitter and delay on microphone arrays. It will be shown that A(2)B allows for a robust data transmission, while ensuring deterministic latency and channels synchronization, thus overcoming the signal integrity issues which usually affect MEMS capsules. The microphone positioning is also discussed since it greatly affects the spatial accuracy of beamforming. Numerical simulations were performed on four regular geometries to identify the optimal layout in terms of number of capsules and beamforming directivity. An A(2)B planar array with equilateral triangle geometry and four microphones, three in the vertices and one in the center, was built. Experimental measurements were performed, obtaining an excellent matching with numerical simulations. Finally, the concept of an array of arrays (meta-array) is presented, designed by combining several triangular units and analyzed through numerical simulations.

关键词： Microphone arrays Array signal processing Geometry Clocks Micromechanical devices arrays Numerical simulation Automotive Audio Bus (A(2)B) automotive applications beamforming consumer products digital MEMS microphones meta-arrays microphone arrays planar arrays spatial audio triangular arrays

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Maximum likelihood estimation for the Frechet distribution based on block maxima extracted from a time series

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BERNOULLI 2018年第2期24卷 1427-1462页

作者： Buecher, Axel Segers, Johan Ruhr Univ Bochum Fak Math Univ Str 150 D-44780 Bochum Germany Catholic Univ Louvain Inst Stat Biostat & Sci Actuarielles Voie Roman Pays 20 B-1348 Louvain La Neuve Belgium

The block maxima method in extreme-value analysis proceeds by fitting an extreme-value distribution to a sample of block maxima extracted from an observed stretch of a time series. The method is usually validated under two simplifying assumptions: the block maxima should be distributed exactly according to an extreme-value distribution and the sample of block maxima should be independent. Both assumptions are only approximately true. The present paper validates that the simplifying assumptions can in fact be safely made. For general triangular arrays of block maxima attracted to the Frechet distribution, consistency and asymptotic normality is established for the maximum likelihood estimator of the parameters of the limiting Frechet distribution. The results are specialized to the common setting of block maxima extracted from a strictly stationary time series. The case where the underlying random variables are independent and identically distributed is further worked out in detail. The results are illustrated by theoretical examples and Monte Carlo simulations.

关键词： asymptotic normality block maxima method heavy tails maximum likelihood estimation stationary time series triangular arrays

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MAXIMA OF BIVARIATE RANDOM VECTORS - BETWEEN INDEPENDENCE AND COMPLETE DEPENDENCE

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STATISTICS & PROBABILITY LETTERS 1994年第5期21卷 385-394页

作者： HUSLER, J UNIV BERN DEPT MATH & STATCH-3012 BERNSWITZERLAND

We analyse the asymptotic dependence structure of bivariate maxima in a triangular array of independent random vectors. This extends the analysis of the classical case of i.i.d. random vectors and the known relationsh... 详细信息

关键词： MAXIMA triangular arrays BIVARIATE RANDOM VECTOR DEPENDENCE BIVARIATE EXTREME VALUE DISTRIBUTIONS

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Higher-order expansions of distributions of maxima in a Husler-Reiss model

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2016年第1期18卷 181-196页

作者： Hashorva, Enkelejd Peng, Zuoxiang Weng, Zhichao Univ Lausanne Fac Business & Econ HEC CH-1015 Lausanne Switzerland Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China

The max-stable Husler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper establishes higher-order asymptotic expansions of the joint distribution of maxima under refined Husler-Reiss conditions. In particular, the rate of convergence of normalized maxima to the Husler-Reiss distribution is explicitly calculated. Our findings are supported by the results of a numerical analysis.

关键词： Husler-Reiss max-stable distribution Higher-order asymptotic expansion triangular arrays Gaussian random vector

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Anomalous Diffusions in Option Prices: Connecting Trade Duration and the Volatility Term Structure

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SIAM JOURNAL ON FINANCIAL MATHEMATICS 2020年第4期11卷 1137-1167页

作者： Jacquier, Antoine Torricelli, Lorenzo Imperial Coll London Dept Math London SW7 2AZ England Univ Parma Dept Econ & Management I-43125 Parma Italy

Anomalous diffusions arise as scaling limits of continuous-time random walks whose innovation times are distributed according to a power law. The impact of a nonexponential waiting time does not vanish with time and leads to different distribution spread rates compared to standard models. In financial modeling this has been used to accommodate random trade duration in the tick-by-tick price process. We show here that anomalous diffusions are able to reproduce the market behavior of the implied volatility more consistently than the usual Levy or stochastic volatility models. Two distinct classes of underlying asset models are analyzed: one with independent price innovations and waiting times, and one allowing dependence between these two components. These models capture the well-known paradigm according to which shorter trade duration is associated with higher return impact of individual trades. We fully describe these processes in a semimartingale setting leading to no-arbitrage pricing formulas, study their statistical properties, and in particular observe that skewness and kurtosis of asset returns do not tend to zero as time goes by. We finally characterize the large-maturity asymptotics of call option prices, and find that the convergence rate to the spot price is slower than in standard Levy regimes, which in turn yields a declining implied volatility term structure and a slower time decay of the skew.

关键词： anomalous diffusions volatility skew term structure derivative pricing CTRWs inverse Levy subordinators time changes Levy processes subdiffusions beta distribution triangular arrays

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Asymptotic stability of the bootstrap sampled mean

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2002年第2期97卷 289-306页

作者： del Barrio, E Cuesta-Albertos, JA Matrán, C Univ Valladolid Fac Ciencias Dept Estadist & Invest Operat E-47002 Valladolid Spain Univ Cantabria Fac Ciencias Dept Matemat Estadist & Computac Cantabria Spain

The asymptotic distribution of the bootstrap sample mean depends on the resampling intensity. This paper explores the sensitivity of that distribution against different resampling intensities. It is generally assumed that small resampling sizes make the bootstrap work. However, we will show that the bootstrap mean can only be highly unstable for small resampling intensities;Our setup considers resampling from a triangular array of row-wise independent and identically distributed random variables satisfying the Central Limit Theorem. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： bootstrap sample mean asymptotic stability asymptotic distribution triangular arrays resampling intensity

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