Greetings, My question is more algorithmic than prectical. What I am
trying to determine is, are the GAM algorithms used in the mgcv package
affected by nonnormally-distributed residuals?
As I understand the theory of linear models the Gauss-Markov theorem
guarantees that least-squares regression is optimal over all unbiased
estimators iff the data meet the conditions linearity, homoscedasticity,
independence, and normally-distributed residuals. Absent the last
requirement it is optimal but only over unbiased linear estimators.
What I am trying to determine is whether or not it is necessary to check
for normally-distributed errors in a GAM from mgcv. I know that the
unsmoothed terms, if any, will be fitted by ordinary least-squares but I
am unsure whether the default Penalized Iteratively Reweighted Least
Squares method used in the package is also based upon this assumption or
falls under any analogue to the Gauss-Markov Theorem.
Thank you in advance for any help.
Sincrely,
Collin Lynch.
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