摘要翻译:
假定随机过程$x=(X_t)_{t\geq0}$是一个强度已知且跳跃大小密度未知的复合Poisson过程$y=(Y_t)_{t\geq0}$和一个独立的布朗运动$z=(Z_t)_{t\geq0}$,我们考虑了从$x的低频观测到的$f$的非参数估计问题。$通过Fourier反演和核平滑构造了$f$的估计量。我们的主要结果是讨论了所提出的估计量在不动点上的渐近正态性。
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英文标题:
《Decompounding under Gaussian noise》
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作者:
Shota Gugushvili
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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: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:
Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$ we consider the problem of nonparametric estimation of $f$ from low frequency observations from $X.$ The estimator of $f$ is constructed via Fourier inversion and kernel smoothing. Our main result deals with asymptotic normality of the proposed estimator at a fixed point.
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PDF链接:
https://arxiv.org/pdf/711.0719