比例风险回归中的局部偏似然估计

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摘要翻译：
Fan,Gijbels和King[Ann.Statist.25(1997)1661-1690]考虑了比例风险模型中风险函数$\psi(x)$的估计。他们提出的估计是基于积分通过局部似然得到的估计导数函数。他们证明了导数函数的大样本性质，但风险函数本身的估计量的大样本性质没有建立。本文考虑任意位置归一化点$x1$的相对风险函数$\psi(x2)-\psi(x1)$的直接估计。我们方法的主要新奇之处在于，当构造局部似然时，我们选择在$x_1$和$x_2$的收缩邻域中的观测，而Fan，Gijbels和King[Ann.Statist.25(1997)1661-1690]只集中在单个邻域上，导致局部似然函数中的风险函数被取消。严格地建立了估计量的渐近性质，并且很容易估计出估计量的方差。我们的方法背后的想法被扩展到估计组之间的差异。进行了仿真研究。
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英文标题：
《Local partial likelihood estimation in proportional hazards regression》
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作者：
Songnian Chen, Lingzhi Zhou
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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：
  Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] considered the estimation of the risk function $\psi (x)$ in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large sample properties of the estimator for the risk function itself were not established. In this paper, we consider direct estimation of the relative risk function $\psi (x_2)-\psi (x_1)$ for any location normalization point $x_1$. The main novelty in our approach is that we select observations in shrinking neighborhoods of both $x_1$ and $x_2$ when constructing a local version of the partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] only concentrated on a single neighborhood, resulting in the cancellation of the risk function in the local likelihood function. The asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated. The idea behind our approach is extended to estimate the differences between groups. A simulation study is carried out.
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PDF链接：
https://arxiv.org/pdf/708.215

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关键词：似然估计 proportional large sample neighborhood concentrated Gijbels King 函数 局部 导数