A STOCHASTIC ESTIMATOR OF THE TRACE OF THE INFLUENCE MATRIX FOR LAPLACIAN SMOOTHING SPLINES
A STOCHASTIC ESTIMATOR OF THE TRACE OF THE INFLUENCE MATRIX FOR LAPLACIAN SMOOTHING SPLINES
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DOI：
10.1080/03610919008812866
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发表时间：
1990-01-01
影响因子：
0.9
通讯作者：
HUTCHINSON, MF
中科院分区：
文献类型：
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作者：
HUTCHINSON, MF
描述了tr（I-A）的一个无偏随机估计，其中A是与Laplacian光滑样条计算有关的影响矩阵。估计是类似于最近开发的吉拉德，但满足最小方差准则，并不需要一个标准的正态变量的模拟。它使用离散随机变量的模拟，每个值取1，-1的概率为1/2。的估计，类似于那些建立由吉拉德的方差的界，使用初等方法获得。估计可以用来近似最小化广义交叉验证（GCV）时，使用离散迭代方法拟合拉普拉斯平滑样条非常大的数据集。模拟的例子表明，估计的迹值，无论是使用这里提出的估计或估计的吉拉德，几乎执行以及精确的值时，适用于最小化的GCV的n小到几百个，其中n是数据点的数量。
An unbiased stochastic estimator of tr(I–A), where A is the influence matrix associated with the calculation of Laplacian smoothing splines, is described. The estimator is similar to one recently developed by Girard but satisfies a minimum variance criterion and does not require the simulation of a standard normal variable. It uses instead simulations of the discrete random variable which takes the values 1, -1 each with probability 1/2. Bounds on the variance of the estimator, similar to those established by Girard, are obtained using elementary methods. The estimator can be used to approximately minimize generalised cross validation (GCV) when using discretized iterative methods for fitting Laplacian smoothing splines to very large data sets. Simulated examples show that the estimated trace values, using either the estimator presented here or the estimator of Girard, perform almost as well as the exact values when applied to the minimization of GCV for n as small as a few hundred, where n is the number of data points.