检索结果-南通市图书馆

On tail behavior of nonlinear autoregressive functional conditional heteroscedastic model with heavy-tailed innovations

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2005年第9期48卷 1169-1181页

作者： PAN Jiazhu WU Guangxu LMAM and School of Mathematical Sciences Peking University Beijing 100871 China LMAM and School of Mathematical Sciences Peking University Beijing 100871 China

We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavytailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.

关键词： tail probability, stationary distribution, nonlinear AR model, nonlinear autoregressive functional conditional heteroscedastic model, heavy-tailed distribution.

An asymptotic relationship for ruin probabilities under heavy-tailed claims

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2002年第5期45卷 632-639页

作者：唐启鹤 Department of Statistics and Finance Univ. of Sci. and Technol. of China Hefei 230026 China

The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy R(x, ∞)～ p-1 e(x) if the claim sizes are heavy-tailed, where Fe denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, p is the safety loading coefficient of the model and the limit process is for x →∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.

关键词： Cramér-Lundberg model, geometric sums, heavy-tailed distribution, ladder height,ruin probabilities.

Robust Variational Bayesian Adaptive Cubature Kalman Filtering Algorithm for Simultaneous Localization and Mapping with heavy-tailed Noise

在线全文

学校读者我要写书评

暂无评论

Journal of Shanghai Jiaotong university(Science) 2020年第1期25卷 76-87页

作者：张铸青董鹏庹红娅刘光军贾鹤 School of Aeronautics and Astronautics Shanghai Jiao Tong UniversityShanghai 200240China Department of Aerospace Engineering Ryerson UniversityTorontoCanada

Simultaneous localization and mapping(SLAM)has been applied across a wide range of areas from robotics to automatic pilot.Most of the SLAM algorithms are based on the assumption that the noise is timeinvariant Gaussian distribution.In some cases,this assumption no longer holds and the performance of the traditional SLAM algorithms declines.In this paper,we present a robust SLAM algorithm based on variational Bayes method by modelling the observation noise as inverse-Wishart distribution with "harmonic mean".Besides,cubature integration is utilized to solve the problem of nonlinear system.The proposed algorithm can effectively solve the problem of filtering divergence for traditional filtering algorithm when suffering the time-variant observation noise,especially for heavy-tai led noise.To validate the algorithm,we compare it with other t raditional filtering algorithms.The results show the effectiveness of the algorithm.

关键词： simultaneous localization and mapping(SLAM) variational Bayesian(VB) heavy-tailed noise robust estimation

heavy-tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied Mathematics 2014年第13期5卷 2050-2056页

作者： Frederic von Wegner Medical Biophysics Group Institute of Physiology and Pathophysiology University of Heidelberg Heidelberg Germany

A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.

关键词： heavy-tailed Distributions Random Sampling Gaussian Exponential Power-Law

Nearly nonstationary processes under infinite variance GARCH noises

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2022年第2期37卷 246-257页

作者： ZHANG Rong-mao LIU Qi-meng SHI Jian-hua School of Mathematics and Statistics Minnan Normal UniversityZhangzhou 363000China School of Mathematical Science Zhejiang UniversityHangzhou 310027China

Let Y_(t) be an autoregressive process with order one,i.e.,Y_(t)=μ+ϕnY_(t-1)+εt,where fεtg is a heavy tailed general GARCH noise with tail indexα.Letϕn be the least squares estimator(LSE)ofϕn.Forμ=0 andα<2,it is shown by Zhang and Ling(2015)thatϕn is inconsistent when Y_(t) is stationary(i.e.,ϕn.,ϕ<1),however,Chan and Zhang(2010)showed thatϕn is still consistent with convergence rate n when Y_(t) is a unit-root process(i.e.,ϕn=1)and fεtg is a GARCH(1,1)noise.There is a gap between the stationary and nonstationary cases.In this paper,two important issues will be considered:(1)what about the nearly unit root case?(2)When canϕbe estimated consistently by the LSE?We show that whenϕn=1-c/n,then bϕn converges to a functional of stable process with convergence rate n.Further,we show that if limn!1 kn(1-ϕn)=c for a positive constant c,then kn(ϕn-ϕ)converges to a functional of two stable variables with tail indexα/2,which means thatϕn can be estimated consistently only when kn!1.

关键词： GARCH noises heavy-tailed stable processes and unit-root

Tail asymptotic for discounted aggregate claims with one-sided linear dependence and general investment return

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2019年第4期62卷 735-750页

作者： Fenglong Guo Dingcheng Wang Jiangsu Key Laboratory of Financial Engineering and School of Finance Nanjing Audit University School of Mathematical Sciences University of Electronic Science and Technology of China

In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with c`adl`ag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.

关键词： Poisson risk model tail probability one-sided linear process heavy-tailed distribution asymptotic upper bound investment return

Local asymptotic behavior of the survival probability of the equilibrium renewal model with heavy tails

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2005年第3期48卷 300-306页

作者： JIANG Tao & CHEN Yiqing School of Finance. Nanjing University of Finance and Economics, Nanjing 210003, China School of Economics and Management, Guangdong University of Technology, Guangzhou 510090, China School of Finance Nanjing University of Finance and Economics Nanjing China School of Economics and Management Guangdong University of Technology Guangzhou China

Recently, Tang established a local asymptotic relation for the ruin probability to the Cram(e)r-Lunbderg risk model.In this short note we extend the corresponding result to the equilibrium renewal risk model.

关键词： geometric sums, heavy-tailed distribution, ladder height, the equilibrium renewal model, the ruin probability.

Asymptotic behavior for sums of non-identically distributed random variables

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2019年第1期34卷 45-54页

作者： YU Chang-jun CHENG Dong-ya School of Sciences Nantong University School of Mathematical Sciences Soochow University The Statistics and Operations Research Department the University of North Carolina at Chapel Hill

For any given positive integer m, let X_i, 1 ≤ i ≤ m be m independent random variables with distributions F_i, 1 ≤ i ≤ m. When all the summands are nonnegative and at least one of them is heavy-tailed, we prove that the lower limit of the ratio ■equals 1 as x →∞. When the summands are real-valued, we also obtain some asymptotic results for the tail probability of the sums. Besides, a local version as well as a density version of the above results is also presented.

关键词： lower limits upper limits heavy-tailed distributions local distributions densities

Double-Penalized Quantile Regression in Partially Linear Models

在线全文

学校读者我要写书评

暂无评论

Open Journal of Statistics 2015年第2期5卷 158-164页

作者： Yunlu Jiang Department of Statistics College of Economics Jinan University Guangzhou China

In this paper, we propose the double-penalized quantile regression estimators in partially linear models. An iterative algorithm is proposed for solving the proposed optimization problem. Some numerical examples illustrate that the finite sample performances of proposed method perform better than the least squares based method with regard to the non-causal selection rate (NSR) and the median of model error (MME) when the error distribution is heavy-tail. Finally, we apply the proposed methodology to analyze the ragweed pollen level dataset.

关键词： Quantile Regression Partially Linear Model heavy-tailed Distribution