What does the alpha argument of the ltsReg function in the robustbase package mean?

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What does the alpha argument of the ltsReg function in the robustbase package mean?

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#1 by (2 votes)

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I have a question about using the alpha argument of the ltsReg function of the robustbase package.

As I understand it, it is responsible for determining the size of the subsets that will be used to fit the model for these subsets, selecting the model of the subset that presented the smallest residues squared.

Generally, the value used for lts is 0.5, but the alpha argument allows you to provide a value between 0.5 and 1. So if I use the value 1, my setting must be equivalent to the OLS setting? Or am I misreading the alpha argument?

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asked by anonymous 31.03.2016 / 18:15

1 answer

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score 2 · Accepted Answer

Estimates should be equivalent when you use alpha = 1 . See the example below:

> library(robustbase)
> data(heart)
> coef(ltsReg(clength ~ height + weight, data = heart, alpha = 1))
 Intercept     height     weight 
20.3757645  0.2107473  0.1910949 
> coef(lm(clength ~ height + weight, data = heart))
(Intercept)      height      weight 
 20.3757645   0.2107473   0.1910949

What may happen is that for ltsReg there is no closed form to obtain the estimates so they are obtained computationally as opposed to simple linear regression. Therefore, differences in approximation may occur.

See the functions that are minimized in simple linear regression:

andinlineartrimmedsquares:

If k = n what happens with alpha = 1 , the functions become equal. Therefore the estimates will also be equal.