smoothm(smoothmest)
smoothm()所属R语言包：smoothmest
Smoothed and unsmoothed 1-d location M-estimators
平滑和平滑的1-D位置的M-估计
译者：生物统计家园网 机器人LoveR
描述----------Description----------
smoothm is an interface for all the smoothed M-estimators introduced in Hampel, Hennig and Ronchetti (2011) for one-dimensional location, the Huber- and Bisquare-M-estimator and the ML-estimator of the Cauchy distribution, calling all the other functions documented on this page.
smoothm是一个接口，用于所有的平滑汉佩尔，Hennig和龙凯蒂（2011）介绍了一维的位置的M-估计的Huber和Bisquare-M-估计和对ML-估计柯西分布调用此页上记录的所有其他职能。
用法----------Usage----------
smoothm(y, method="smhuber",
k=0.862, sn=sqrt(2.046/length(y)),
tol=1e-06, s=mad(y), init="median")
sehuber(y, k = 0.862, tol = 1e-06, s=mad(y), init="median")
smhuber(y, k = 0.862, sn=sqrt(2.046/length(y)), tol = 1e-06, s=mad(y),
smmed=FALSE, init="median")
mbisquare(y, k=4.685, tol = 1e-06, s=mad(y), init="median")
smbisquare(y, k=4.685, tol = 1e-06, sn=sqrt(1.0526/length(y)),
s=mad(y), init="median")
mlcauchy(y, tol = 1e-06, s=mad(y))
smcauchy(y, tol = 1e-06, sn=sqrt(2/length(y)), s=mad(y))
参数----------Arguments----------
参数：y
numeric vector. Data set.
数字矢量。数据集。
参数：method
one of "huber", "smhuber", "bisquare", "smbisquare", "cauchy", "smcauchy", "smmed". See details.
"huber"，"smhuber"，"bisquare"，"smbisquare"，"cauchy"，"smcauchy"，"smmed"之一。查看详细信息。
参数：k
numeric. Tuning constant. This is used for method one of "huber", "smhuber", "bisquare", "smbisquare" in smoothm and the corresponding functions. Tuning constants are defined for the Huber- and Bisquare M-estimator as in Maronna et al. (2006). The default values refer to a Huber M-estimator which is optimal under 20% contamination (0.862) and to a Bisquare M-estimator with 95% efficiency under the Gaussian model (4.685).
数字。时间常数。这是用于method之一"huber", "smhuber", "bisquare", "smbisquare"中smoothm和相应的功能。调整常量定义的胡贝尔和Bisquare M-估计在Maronna等。 （2006年）。默认值是指休伯M-估计下是最佳的20％的污染（0.862）和一个Bisquare M-估计根据高斯模型（4.685）与95％的效率。
参数：sn
numeric. This is used for method one of "smhuber", "smbisquare", "smcauchy", "smmed". This is the smoothing standard error σ_n in Hampel et al. (2011) depending on the sample size and the asymptotic variance of the base estimator. The default value of smoothm and smhuber is based on a Huber estimator with k=0.862 under Huber's least favourable distribution for which it is ML. The default value of smbisquare is based on the Bisquare estimator with k=4.685 under the Gaussian distribution. The default value of smcauchy is based on the Cauchy ML estimator under the Cauchy distribution. A value that can be used for the smoothed median is sqrt(1.056/length(y)), which is based on the median under the double exponential (Laplace) distribution with 1.4826 MAD=1. Note that the distributional "assumptions" for these choices are by no means critical; they should work well under many other distributions as well.
数字。这是用于method1"smhuber", "smbisquare", "smcauchy", "smmed"。这是平滑的标准误差σ_n汉佩尔等。 （2011）根据样本的大小和碱基估计的渐近方差。默认值smoothm和smhuber休伯k=0.862下Huber的最有利的分布，它是ML估计的基础上。 smbisquare的默认值是基于与k=4.685下的高斯分布的，在Bisquare估计。是基于柯西分布的的柯西ML估计下的默认值smcauchy。甲可用于被平滑的中位数的值，该值是的sqrt(1.056/length(y))，它是基于根据与1.4826 MAD = 1的双指数（拉普拉斯）分布的中位数。请注意，这些选择的分配“假设”绝不是关键，他们应能承受工作上的许多其他分派。
参数：tol
numeric. Stopping criterion for algorithms (absolute difference between two successive values).
数字。停止准则的算法（绝对连续两个值之间的差异）。
参数：s
numeric. Estimated or assumed scale/standard deviation.
数字。估计或假设的规模/标准差。
参数：init
"median" or "mean". Initial estimator for iteration. Ignored if method=="cauchy" or "smcauchy".
"median"或"mean"。初步估计迭代。如果method=="cauchy"或"smcauchy"忽略。
参数：smmed
logical. If FALSE, the smoothed Huber estimator is computed, otherwise the smoothed median by smhuber.
逻辑。如果FALSE，平滑的胡贝尔估计计算，否则，平滑的中位数smhuber。
Details
详细信息----------Details----------
The following estimators can be computed (some computational details are given in Hampel et al. 2011):
下面的估计，可以计算（汉佩尔等人给出了一些计算细节。2011）：
Huber estimator.method="huber" and function sehuber compute the standard Huber estimator (Huber and Ronchetti 2009). The only differences from huber are that s and init can be specified and that the default k is different.
胡伯估计。method="huber"和函数sehuber计算标准估计胡伯（Huber和龙凯蒂2009）。从HUBER唯一的区别是，s和init可以指定的默认k是不同的。
Smoothed Huber estimator.method="smhuber" and function smhuber compute the smoothed Huber estimator (Hampel et al. 2011).
平滑胡贝尔估计。method="smhuber"和功能smhuber计算的平滑估计胡贝尔（汉佩尔等2011）。
Bisquare estimator.method="bisquare" and function bisquare compute the bisquare M-estimator (Maronna et al. 2006). This uses psi.bisquare.
是Bisquare估计。method="bisquare"和函数bisquare计算的bisquare的M-估计（Maronna等，2006）。这里使用psi.bisquare。
Smoothed bisquare estimator.method="smbisquare" and function smbisquare compute the smoothed bisquare M-estimator (Hampel et al. 2011). This uses psi.bisquare
平滑bisquare估计。method="smbisquare"和功能smbisquare计算的平滑bisquare M-估计（汉佩尔等2011）。使用psi.bisquare
ML estimator for Cauchy distribution.method="cauchy" and function mlcauchy compute the ML-estimator for the Cauchy distribution.
ML估计柯西分布。method="cauchy"和功能mlcauchy柯西分布计算ML估计。
Smoothed ML estimator for Cauchy distribution.method="smcauchy" and function smcauchy compute the smoothed ML-estimator for the Cauchy distribution (Hampel et al. 2011).
柯西分布平滑似然估计。method="smcauchy"和函数smcauchy计算平滑ML估计柯西分布（汉佩尔等2011）。
Smoothed median.method="smmed" and function smhuber with median=TRUE compute the smoothed median (Hampel et al. 2011).
平滑位数。method="smmed"和函数smhuber与median=TRUE计算平滑的中位数（汉佩尔等2011）。
值----------Value----------
A list with components <table summary="R valueblock"> <tr valign="top"><td>mu</td> <td> the location estimator.</td></tr> <tr valign="top"><td>method</td> <td> see above.</td></tr> <tr valign="top"><td>k</td> <td> see above.</td></tr> <tr valign="top"><td>sn</td> <td> see above.</td></tr> <tr valign="top"><td>tol</td> <td> see above.</td></tr> <tr valign="top"><td>s</td> <td> see above.</td></tr> </table>
组件的列表<table summary="R valueblock"> <tr valign="top"> <TD> mu</ TD> <TD>的位置估计。</ TD> </ TR> <TR VALIGN =“顶”> <TD>method </ TD> <TD>上面看到的。</ TD> </ TR> <tr valign="top"> <TD>k</ TD> <TD>上面看到的。</ TD> </ TR> <tr valign="top"> <TD>sn </ TD> <TD>上面看到的。</ TD> </ TR> <tr valign="top"> <TD> tol </ TD> <TD>上面看到的。</ TD> </ TR> <tr valign="top"> <TD>s </ TD> <TD>上面看到的。</ TD> </ TR> </ TABLE>
（作者）----------Author(s)----------
Christian Hennig
<a href="mailto:chrish@stats.ucl.ac.uk">chrish@stats.ucl.ac.uk</a>
<a href="http://www.homepages.ucl.ac.uk/~ucakche/">http://www.homepages.ucl.ac.uk/~ucakche/</a>
参考文献----------References----------
Hampel, F., Hennig, C. and Ronchetti, E. (2011) A smoothing principle for the Huber and other location M-estimators. Computational Statistics and Data Analysis 55, 324-337.
Huber, P. J. and Ronchetti, E. (2009) Robust Statistics (2nd ed.). Wiley, New York.
Maronna, A.R., Martin, D.R., Yohai, V.J. (2006). Robust Statistics: Theory and Methods. Wiley, New York
参见----------See Also----------
pitman, huber, rlm
pitman，huber，rlm
实例----------Examples----------
library(MASS)
set.seed(10001)
y <- rdoublex(7)
median(y)
huber(y)$mu
smoothm(y)$mu
smoothm(y,method="huber")$mu
smoothm(y,method="bisquare",k=4.685)$mu
smoothm(y,method="smbisquare",k=4.685,sn=sqrt(1.0526/7))$mu
smoothm(y,method="cauchy")$mu
smoothm(y,method="smcauchy",sn=sqrt(2/7))$mu
smoothm(y,method="smmed",sn=sqrt(1.0526/7))$mu
smoothm(y,method="smmed",sn=sqrt(1.0526/7),init="mean")$mu
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-30 10:31:20
