lmrob(robustbase)
lmrob()所属R语言包：robustbase
MM-type Estimators for Linear Regression
MM型估计的线性回归
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Computes fast MM-type estimators for linear (regression) models.
计算速度快的MM型估计的线性模型（回归）。
用法----------Usage----------
lmrob(formula, data, subset, weights, na.action, method = "MM",
model = TRUE, x = !control$compute.rd, y = FALSE,
singular.ok = TRUE, contrasts = NULL, offset = NULL,
control = NULL, init = NULL, ...)
参数----------Arguments----------
参数：formula
a symbolic description of the model to be fit. See lm and formula for more details.
一个象征性的模型来描述是合适的。 lm和formula更多的细节。
参数：data
an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lmrob is called.
一个可选的数据框，列表或环境（或as.data.frame到数据框的对象强制转换），其中包含在模型中的变量。如果没有找到data，变量environment(formula)，通常是lmrob被称为环境。
参数：subset
an optional vector specifying a subset of observations to be used in the fitting process.
一个可选的矢量指定的装配过程中可以使用的观测值的一个子集。
参数：weights
an optional vector of weights to be used in the fitting process.
在嵌合过程中要使用可选的权重向量。
参数：na.action
a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The “factory-fresh” default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.
一个函数，它表示当数据包含NA的，应该发生什么。默认设置是由na.action的options，是na.fail，如果是没有设置的。 “出厂时的默认是na.omit。另一种可能的值是NULL，没有行动。值na.exclude可能是有用的。
参数：method
string specifying the estimator-chain. MM is interpreted as SM. See Details.
字符串，该字符串指定的估计链。 MM被解释为SM。查看详细信息。
参数：model, x, y
logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, the response) are returned.
的逻辑。如果TRUE拟合（模型框架，模型矩阵，响应）的相应部件返回。
参数：singular.ok
logical. If FALSE (the default in S but not in R) a singular fit is an error.
逻辑。如果FALSE（默认情况下，在S，但R）一个奇异的配合是一个错误。
参数：contrasts
an optional list. See the contrasts.arg of model.matrix.default.
可选列表。请参阅contrasts.argmodel.matrix.default。
参数：offset
this can be used to specify an a priori known component to be included in the linear predictor during fitting. An offset term can be included in the formula instead or as well, and if both are specified their sum is used.
这可以被用来指定一个先验已知的组件被包括在配合期间的线性预测。式，而不是，或也可以包括在一个offset术语，和如果两者都指定使用它们的总和。
参数：control
a list specifying control parameters; use the function lmrob.control(.) and see its help page.
一个list指定控制参数;使用的功能lmrob.control(.)，看看它的帮助页。
参数：init
an optional argument to specify or supply the initial estimate. See Details.
一个可选的参数指定或提供的初步估计。查看详细信息。
参数：...
can be used to specify control parameters directly instead of via control.
可用于指定控制参数，而不是直接通过control。
Details
详细信息----------Details----------
This function computes an MM-type regression estimator as described in Yohai (1987) and Koller and Stahel (2011). By default it uses a bi-square redescending score function, and it returns a highly robust and highly efficient estimator (with 50% breakdown point and 95% asymptotic efficiency for normal errors). The computation is carried out by a call to lmrob.fit().
此函数计算MM-型回归估计，在Yohai（1987）和科勒和Stahel（2011）。默认情况下，使用一个双方redescending的得分函数，并返回一个高度可靠和高效率的估计，50％的故障点和95％的一般错误的渐近效率。的计算进行通过调用lmrob.fit()。
The argument setting of lmrob.control is provided to set alternative defaults as suggested in Koller and Stahel (2011) (use setting='KS2011'). For details, see lmrob.control.
参数settinglmrob.control提供的建议来替代默认设置在科勒和Stahel（2011）（使用setting='KS2011'）。有关详细信息，请参阅lmrob.control。
The initial estimator may be specified using the argument init. This argument can either be a string, a function or a list. A string can be used to specify built in internal estimators (currently S and M-S, see See also below). A function taking arguments x, y, control, mf (where mf stands for model.frame) and returning a list containing at least the initial coefficients as coefficients and the initial scale estimate scale. Or a list giving the initial coefficients and scale as coefficients and scale. See also Examples.
初步估计可以指定使用参数init。此参数可以是一个字符串，函数的列表。目前，一个字符串可以被用来指定建立在内部估计（S和M-S，见也见下文）。一个函数参数x, y, control, mf（其中mf的model.frame），并返回一个列表，其中包含的初始系数为coefficients和初始规模估计scale的，至少 。或者一个列表，给出的初始系数和规模coefficients和scale。另见的例子。
Note that if the init argument supplied is a function or list, the method argument must not contain the initial estimator, e.g., use MDM instead of SMDM.
请注意，如果提供的初始化参数是一个函数或列表，方法的参数必须不包含初步估计，例如，使用MDM而不是SMDM。
The default, equivalent to init = "S", uses as initial estimator an S-estimator (Rousseeuw and Yohai, 1984) which is computed using the Fast-S algorithm of Salibian-Barrera and Yohai (2006), calling lmrob.S(). That function, since March 2012, uses nonsingular subsampling which makes the Fast-S algorithm feasible for categorical data as well.
默认情况下，相当于init = "S"，使用的S-估计的（Rousseeuw和Yohai，1984年），这是计算的快速算法-S Salibian巴雷拉和Yohai的（2006）初步估计，调用lmrob.S() 。 ，自2012年3月，该函数的快速算法是可行的分类数据以及使用非奇异二次抽样。
The following chain of estimates is customizable via the method argument. There are currently two types of estimates available,
以下链的估计是可自定义的，通过method参数。估计目前有两种类型，
"M": corresponds to the standard M-regression
"M"：对应于标准的M-回归
"D": stands for the Design Adaptive Scale estimate
"D"：代表设计自适应的规模估算
The method argument takes a string that specifies the estimates to be calculated as a chain. Setting method='SMDM' will result in an intial S-estimate, followed by an M-estimate, a Design Adaptive Scale estimate and a final M-step. For methods involving a D-step, the default value of psi (see lmrob.control) is changed to "lqq".
method参数需要一个字符串，指定链的估计来计算。设置method='SMDM'将导致S-估计在一个INTIAL的，然后由一个M-估计，设计尺度自适应估计和一个最终的M步。对于涉及D步，默认值psi（lmrob.control）的方法改变"lqq"。
By default, standard errors are computed using the formulas of Croux, Dhaene and Hoorelbeke (2003) (lmrob.control option cov=".vcov.avar1"). This method, however, works only for MM-estimates. For other method arguments, the covariance matrix estimate used is based on the asymptotic normality of the estimated coefficients (cov=".vcov.w") as described in Koller and Stahel (2011).
默认情况下，标准误差计算使用的公式，克鲁，Dhaene和Hoorelbeke（2003年）（lmrob.control“选项”cov=".vcov.avar1"）。但这种方法仅适用于MM估计。其他method参数，协方差矩阵的估计是基于渐近正态性的估计系数（cov=".vcov.w"）作为描述的在科勒和Stahel（2011）。
值----------Value----------
An object of class lmrob. A list that includes the following components:
对象的类lmrob。一个列表，包含以下组件：
参数：coefficients
The estimate of the coefficient vector
的系数向量的估计
参数：init.S
The list returned by lmrob.S or lmrob.M.S (for MM-estimates only)
返回的列表lmrob.S或lmrob.M.S（MM估计只有）
参数：init
A similar list that contains the results of intermediate estimates (not for MM-estimates).
类似的列表，其中包含中间的估计结果（MM估计）。
参数：scale
The scale as used in the M estimator.
M估计中所使用的规模。
参数：cov
The estimated covariance matrix of the regression coefficients
回归系数的估计协方差矩阵
参数：residuals
Residuals associated with the estimator
估计器与相关联的残差
参数：fitted.values
Fitted values associated with the estimator
与估计的拟合值
参数：weights
the “robustness weights” ψ(r_i/S) / (r_i/S).
“鲁棒性权重”ψ(r_i/S) / (r_i/S)。
参数：converged
TRUE if the IRWLS iterations have converged
TRUE，如果IRWLS迭代收敛
（作者）----------Author(s)----------
Matias Salibian-Barrera and Manuel Koller
参考文献----------References----------
Robust standard errors for robust estimators, Discussion Papers Series 03.16, K.U. Leuven, CES.
robust regression for small samples, Computational Statistics & Data Analysis 55(8), 2504–2515.
Robust regression with both continuous and categorical predictors. Journal of Statistical Planning and Inference 89, 197–214.
Robust regression by means of S-estimators, In Robust and Nonlinear Time Series, J. Franke, W. H盲rdle and R. D. Martin (eds.). Lectures Notes in Statistics 26, 256–272, Springer Verlag, New York.
A fast algorithm for S-regression estimates, Journal of Computational and Graphical Statistics, 15(2), 414–427.
High breakdown-point and high efficiency estimates for regression. The Annals of Statistics 15, 642–65.
参见----------See Also----------
lmrob.control; for the algorithms lmrob.S, lmrob.M.S and lmrob.fit; and for methods, predict.lmrob, summary.lmrob, print.lmrob, and plot.lmrob.
lmrob.control;的算法lmrob.S，lmrob.M.S和lmrob.fit;的方法，predict.lmrob，summary.lmrob，print.lmrob，和plot.lmrob。
实例----------Examples----------
data(coleman)
set.seed(0)
summary( m1 <- lmrob(Y ~ ., data=coleman) )
summary( m2 <- lmrob(Y ~ ., data=coleman, setting = 'KS2011') )
data(starsCYG, package = "robustbase")
## Plot simple data and fitted lines[＃图简单的数据和拟合线]
plot(starsCYG)
lmST <- lm(log.light ~ log.Te, data = starsCYG)
(RlmST <- lmrob(log.light ~ log.Te, data = starsCYG))
abline(lmST, col = "red")
abline(RlmST, col = "blue")
summary(RlmST)
vcov(RlmST)
stopifnot(all.equal(fitted(RlmST),
predict(RlmST, newdata = starsCYG),
tol = 1e-14))
## --- init argument[＃---初始化参数]
## string[＃字符串]
set.seed(0)
m3 <- lmrob(Y ~ ., data=coleman, init = "S")
stopifnot(all.equal(m1[-17], m3[-17]))
## function[＃函数]
initFun <- function(x, y, control, mf) {
init.S <- lmrob.S(x, y, control)
list(coefficients=init.S$coef, scale = init.S$scale)
}
set.seed(0)
m4 <- lmrob(Y ~ ., data=coleman, method = "M", init = initFun)
## list[＃列表]
m5 <- lmrob(Y ~ ., data=coleman, method = "M",
init = list(coefficients = m3$init$coef, scale = m3$scale))
stopifnot(all.equal(m4[-17], m5[-17]))
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注：
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发表于 2012-9-27 22:11:11
