摘要翻译:
在函数线性回归中,斜率参数是一个函数。因此,在非参数上下文中,它是由无穷多个未知数决定的。它的估计涉及解决一个不适定问题,并与一系列方法有接触点,包括统计平滑和反卷积。估计斜率函数的标准方法明确地基于泛函主成分分析,从而基于特征值和特征函数的谱分解。我们对该方法进行了详细的讨论,并证明了在某些情况下,PCA技术可以获得最优的收敛速度。提出了一种基于二次正则化的替代方法,并从某些角度证明了该方法的优越性。
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英文标题:
《Methodology and convergence rates for functional linear regression》
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作者:
Peter Hall, Joel L. Horowitz
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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 functional linear regression, the slope ``parameter'' is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of contact with a range of methodologies, including statistical smoothing and deconvolution. The standard approach to estimating the slope function is based explicitly on functional principal components analysis and, consequently, on spectral decomposition in terms of eigenvalues and eigenfunctions. We discuss this approach in detail and show that in certain circumstances, optimal convergence rates are achieved by the PCA technique. An alternative approach based on quadratic regularisation is suggested and shown to have advantages from some points of view.
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PDF链接:
https://arxiv.org/pdf/708.0466