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摘要翻译：
在纵向和空间研究中，观测结果往往显示出在时间或距离上静止的强相关性，这些数据被采样的时间或位置可能不是均匀的。我们提出了一个非参数估计的相关函数在这样的数据，使用核方法。当被摄体数目固定且每个被摄体中的向量或函数数目为无穷大时，我们给出了所提估计量的逐点渐近正态分布。基于渐近理论，我们提出了一种加权分块自举方法来推断相关函数，其中权值考虑了时间或位置分布的不均匀性。将该方法应用于结肠癌发生研究中的一个数据集，在实验中，从12只大鼠的每一个结肠节段中提取结肠隐窝，然后测量每个隐窝中的细胞周期重要蛋白p27的表达水平。仿真结果也说明了该方法的数值性能。
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英文标题：
《Nonparametric estimation of correlation functions in longitudinal and
spatial data, with application to colon carcinogenesis experiments》
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作者：
Yehua Li, Naisyin Wang, Meeyoung Hong, Nancy D. Turner, Joanne R.
Lupton, Raymond J. Carroll
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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：
In longitudinal and spatial studies, observations often demonstrate strong correlations that are stationary in time or distance lags, and the times or locations of these data being sampled may not be homogeneous. We propose a nonparametric estimator of the correlation function in such data, using kernel methods. We develop a pointwise asymptotic normal distribution for the proposed estimator, when the number of subjects is fixed and the number of vectors or functions within each subject goes to infinity. Based on the asymptotic theory, we propose a weighted block bootstrapping method for making inferences about the correlation function, where the weights account for the inhomogeneity of the distribution of the times or locations. The method is applied to a data set from a colon carcinogenesis study, in which colonic crypts were sampled from a piece of colon segment from each of the 12 rats in the experiment and the expression level of p27, an important cell cycle protein, was then measured for each cell within the sampled crypts. A simulation study is also provided to illustrate the numerical performance of the proposed method.
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PDF链接：
https://arxiv.org/pdf/710.3638
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