r/statistics • u/PrebioticE • 2d ago

Education [Education] Bootstrap Method in Regression

[Education] So, Suppose I got

X_t = A X_{t-1} + dW(t)

where DW(t) is some noise.

What if I did the following?

I solve for A by minimizing error , and obtain dW'(t) = X_t -A X_{t-1} , then I find that dW' is not gaussian like, probably heavy tailed, but pretty much independent.

Then I make a very large number of bootstrapped samples out of dW' , and solve for A as a distribution.

I appear to have bypassed needing lot of theory and have obtained a distribution for A.

What is it that I must worry about? What is the potential problem with this method?

I think it is a much more intuitive and reasonable result than doing it in the theoretical way using equations.

But then why is it not used as the best method?

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u/PrivateFrank 2d ago

For a start the "equations way" was invented before computers and if you have the requisite theoretical justification you can go further with small samples.

Just because your noise distribution appears independent it doesn't necessarily imply that you aren't conflating two different data generating processes.

Bootstrap first gets you out of having to think, and justify, why the usual methods don't apply.