<!doctype s-function-doc system "s-function-doc.dtd" [
<!entity % S-OLD "INCLUDE">
]
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<s-function-doc>
<s-topics>
   <s-topic>test.lmRob</s-topic>
</s-topics>
<s-title>
Various Tests of Robust Regression Estimates 
</s-title>
<s-description>
Conducts test for bias of robust MM-estimates and Least Squares (LS) 
estimates against S-estimates, or permutation test of the slope 
estimate in a straight line fit. 
</s-description>
<s-usage>
<s-old-style-usage>
test.lmRob(object, type="bias", level=NULL) 
</s-old-style-usage>
</s-usage>
<s-args-required>
<s-arg name="object">
an object of class <s-expression>"lmRob"</s-expression>. 
</s-arg>
</s-args-required>
<s-args-optional>
<s-arg name="type">
character string. Valid choices are <s-expression>"bias"</s-expression> for bias test, or 
"permutation" for permutation test. 
</s-arg>
<s-arg name="level">
the level of the test for bias of MM-estimate. By default, the <s-expression>level</s-expression> 
component of <s-expression>object$robust.control</s-expression> is used. 
</s-arg>
</s-args-optional>
<s-value>
the p-value of the permutation test, or an object of class <s-expression>"biasMM"</s-expression>  
representing the bias test, in which case the following components must be 
included: 
<s-return-component name="mm">
a list describing the test of bias for final MM-estimates, with the  
following components: <s-expression>stat</s-expression>, the t-statistic; <s-expression>pchi</s-expression>, the probability  
that a chi-squared random variable with degrees of freedom equal to  
<s-expression>object$rank</s-expression> is smaller than <s-expression>stat</s-expression>; <s-expression>qchi</s-expression>, the quantile of the  
chi-squared distribution with degrees of freedom equal to <s-expression>object$rank</s-expression> 
corresponding to the probability input in the level (<s-expression>object$robust.control$level</s-expression>). 
</s-return-component>
<s-return-component name="ls">
a list describing the test of bias for LS-estimates, with the following   
components: <s-expression>stat</s-expression>, the t-statistic; <s-expression>pchi</s-expression>, the probability that a  
chi-squared random variable with degrees of freedom equal to <s-expression>object$rank</s-expression> 
is smaller than <s-expression>stat</s-expression>. 
</s-return-component>
<s-return-component name="level">
the level of the test for bias of MM-estimate. 
</s-return-component>
</s-value>
<s-section name=" REFERENCES">

Yohai, V., Stahel, W. A., and Zamar, R. H. (1991). A procedure for robust  
estimation and inference in linear regression, in Stahel, W. A. and  
Weisberg, S. W., Eds.,  
<it>Directions in robust statistics and diagnostics, Part II. </it>
Springer-Verlag. 
</s-section>
<s-keywords>
<s-keyword>robust</s-keyword>
<s-keyword>regression</s-keyword>
<s-keyword>librobust</s-keyword>
</s-keywords>
<s-docclass>
function
</s-docclass>
</s-function-doc>
