摘要翻译：
在过去的二十年里，单指标模型作为投影寻踪回归的一种特例，被证明是解决非参数回归中高维问题的有效方法。本文研究了基于弱相关样本的单指标预测(SIP)模型，该模型对单指标模型的偏差具有鲁棒性。通过响应变量的多元预测函数的最佳逼近来识别单指标，而不管预测函数是否是真正的单指标函数。对单指标预测系数提出了一种多项式样条估计，并证明了该估计是n根相合的和渐近正态的。采用迭代优化程序，使用户能够在几秒钟内分析高维的大数据。仿真实验为渐近理论提供了有力的证据。将所提出的程序应用于冰岛的rive流量数据，得到了优越的样本外滚动预报。
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英文标题：
《Spline Single-Index Prediction Model》
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作者：
Li Wang and Lijian Yang
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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：
  For the past two decades, single-index model, a special case of projection pursuit regression, has proven to be an efficient way of coping with the high dimensional problem in nonparametric regression. In this paper, based on weakly dependent sample, we investigate the single-index prediction (SIP) model which is robust against deviation from the single-index model. The single-index is identified by the best approximation to the multivariate prediction function of the response variable, regardless of whether the prediction function is a genuine single-index function. A polynomial spline estimator is proposed for the single-index prediction coefficients, and is shown to be root-n consistent and asymptotically normal. An iterative optimization routine is used which is sufficiently fast for the user to analyze large data of high dimension within seconds. Simulation experiments have provided strong evidence that corroborates with the asymptotic theory. Application of the proposed procedure to the rive flow data of Iceland has yielded superior out-of-sample rolling forecasts.
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PDF链接：
https://arxiv.org/pdf/704.0302