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Estimating curves and derivatives with parametric penalized spline smoothing

机译：用参数惩罚样条平滑法估计曲线和导数

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摘要

Accurate estimation of an underlying function and its derivatives is one of the central problems in statis-tics. Parametric forms are often proposed based on the ex-pert opinion or prior knowledge of the underlying func-tion. However, these strict parametric assumptions may re-sult in biased estimates when they are not completely accu-rate. Meanwhile, nonparametric smoothing methods, which do not impose any parametric form, are quite flexible. We propose a parametric penalized spline smoothing method, which has the same flexibility as the nonparametric smooth-ing methods. It also uses the prior knowledge of the under-lying function by defining an additional penalty term using the distance of the fitted function to the assumed parametric function. Our simulation studies show that the parametric penalized spline smoothing method can obtain more accu-rate estimates of the function and its derivatives than the pe-nalized spline smoothing method. The parametric penalized spline smoothing method is also demonstrated by estimating the human height function and its derivatives from the real data.
机译：对基本函数及其导数的准确估计是统计中的中心问题之一。通常根据专家的意见或对基础功能的先验知识提出参数形式。但是，当这些严格的参数假设不完全准确时，它们可能会导致偏差估计。同时，不施加任何参数形式的非参数平滑方法非常灵活。我们提出了一种参数惩罚样条平滑方法，它具有与非参数平滑方法相同的灵活性。它还通过使用拟合函数到假定参数函数的距离来定义附加惩罚项，从而利用了底层函数的先验知识。我们的仿真研究表明，与惩罚样条平滑方法相比，参数惩罚样条平滑方法可以获得更精确的函数及其导数估计。通过从实际数据中估计人的身高函数及其导数，也证明了参数化惩罚样条平滑方法。

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  • 来源
    《Statistics and computing》 |2012年第5期|p.1059-1067|共9页
  • 作者

    Jiguo Cao; Jing Cai; Liangliang Wang;

  • 作者单位

    Department of Statistics & Actuarial Science, Simon Fraser University, Burnaby, BC, Canada V5A 1S6;

    Department of Statistics & Actuarial Science, Simon Fraser University, Burnaby, BC, Canada V5A 1S6;

    Department of Statistics, University of British Columbia,Vancouver, BC, Canada V6T 1Z2;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    growth curve; nonlinear regression; parameter cascading;

    机译：增长曲线非线性回归参数级联;

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