CHANGE-POINTS IN NONPARAMETRIC REGRESSION-ANALYSIS
CHANGE-POINTS IN NONPARAMETRIC REGRESSION-ANALYSIS
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DOI：
10.1214/aos/1176348654
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发表时间：
1992-06-01
影响因子：
4.5
通讯作者：
MULLER, HG
中科院分区：
文献类型：
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作者：
MULLER, HG
提出了平滑回归模型中不连续点或变点的位置和大小的估计量。所需的假设要比参数模型中的假设弱得多。所提出的估计量也适用于导数的不连续检测，因此也适用于斜率和高阶曲率的变化点检测。所提出的估计是基于左右单侧核平滑的比较。对于变点位置估计量的适当缩放版本，建立了随机过程对高斯过程的局部差的弱收敛性。然后可以利用连续映射定理得到变点估计量的渐近分布和相应的收敛速率。这些速率通常比n-1/2快。通过适当的核修正，推导出曲线估计的全局L(p)收敛率，以适应估计的变化点。结果表明，当改变点的位置已知时，这些收敛速度是相同的。这些方法用1871年至1970年尼罗河年流量的著名数据加以说明。
Estimators for location and size of a discontinuity or change-point in an otherwise smooth regression model are proposed. The assumptions needed are much weaker than those made in parametric models. The proposed estimators apply as well to the detection of discontinuities in derivatives and therefore to the detection of change-points of slope and of higher order curvature. The proposed estimators are based on a comparison of left and right one-sided kernel smoothers. Weak convergence of a stochastic process in local differences to a Gaussian process is established for properly scaled versions of estimators of the location of a change-point. The continuous mapping theorem can then be invoked to obtain asymptotic distributions and corresponding rates of convergence for change-point estimators. These rates are typically faster than n-1/2. Rates of global L(p) convergence of curve estimates with appropriate kernel modifications adapting to estimated change-points are derived as a consequence. It is shown that these rates of convergence are the same as if the location of the change-point was known. The methods are illustrated by means of the well known data on the annual flow volume of the Nile river between 1871 and 1970.