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#1
05-11-2006, 05:50 AM
 Luna Member Join Date: Jan 2006 Posts: 31
Robust estimators

This might sound stupid, but can somebody give me the definition of a robust estimator? I cannot seem to find it in the Loss Models text...
#2
05-11-2006, 07:58 AM
 NewTubaBoy Member CAS Join Date: Jul 2004 Location: Boston Studying for CAS 8 Favorite beer: Blue Moon Posts: 1,391

never even heard of it.
#3
05-11-2006, 08:54 AM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College 1962 (!) Posts: 1,732

A robust estimator is one that performs well even if your model is incorrect. For example, if you foolishly model every random variable by and ExpRV with mean theta determined by MLE and then estimate the mean by theta , since the MLE's theta is the sample mean it performs well even when the variable is not actually Exponential. On the other hand, estimating the variance by theta^2 performs poorly unless the variable truly is Exponential.

Jim Daniel
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#4
05-11-2006, 10:44 AM
 Luna Member Join Date: Jan 2006 Posts: 31

Prof. Daniel,
Thank you for your response.

I'm trying to understand problem 14 in May 2000. The problem asks:

Which of the following statements about evaluating an estimator is false?

and the correct answer is:

(E) A robust estimator is one that performs well even with sampling error.

From your definition, Prof. Daniel, an estimator is robust if it performs well even if your model is incorrect. What's the difference between having an incorrect model and having sample errors?

Thanks for your help...
#5
05-11-2006, 10:50 AM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College 1962 (!) Posts: 1,732

The correctness of the model has nothing to do with the nature of the sample values.

Jim Daniel
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Jim Daniel
Jim Daniel's Actuarial Seminars
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