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摘要翻译：
本文研究了一类随机过程$\{x_t\}_{t\In\n}$,其中$x_t=(\phi\circ T_s^t)(X_0)$由变换T_s的迭代得到，变换T_s对[0,1]上的遍历概率mu_s不变，连续的分部函数$\phi:[0,1]\到\r$。这里我们考虑$T_s:[0,1]\到[0,1]$的Manneville-Pomeau变换。所得过程的自相关函数呈双曲（或多项式）衰减，我们得到了从有限时间序列估计参数s的有效方法。因此，我们还估计了这些过程的自相关衰减的收敛速度。比较了基于周期图函数、平滑周期图函数、部分和方差和小波理论的不同估计方法。
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英文标题：
《Parameter Estimation in Manneville-Pomeau Processes》
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作者：
B. P. Olbermann, Silvia R. C. Lopes and Artur O. Lopes
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
In this work we study a class of stochastic processes $\{X_t\}_{t\in\N}$, where $X_t = (\phi \circ T_s^t)(X_0)$ is obtained from the iterations of the transformation T_s, invariant for an ergodic probability \mu_s on [0,1] and a continuous by part function $\phi:[0,1] \to \R$. We consider here $T_s:[0,1]\to [0,1]$ the Manneville-Pomeau transformation. The autocorrelation function of the resulting process decays hyperbolically (or polynomially) and we obtain efficient methods to estimate the parameter s from a finite time series. As a consequence we also estimate the rate of convergence of the autocorrelation decay of these processes. We compare different estimation methods based on the periodogram function, on the smoothed periodogram function, on the variance of the partial sum and on the wavelet theory.
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PDF链接：
https://arxiv.org/pdf/707.16
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