摘要：Why is ridge regression (RR) often a useful method even in cases where multiple
linear regression (MLR) is dubious or inadequate as a model? We suggest that
some light can be shed on this question if one notes that RR is an application of
Tikhonov regularization (TR), a method that has been explored in the approximation
theory literature for about as long as RR has been used in statistics.
TR has proven useful for many inverse problems, but it has often been applied
without stating a statistical model at all.
In order to indicate how alternatives to MLR might be defined, we give a
subjective overview of some inverse problems from the geophysical sciences. We
conclude that estimation is often at least as important as prediction.
Key words: inverse problems, Tikhonov regularization, partial least squares,
principal components regression, regularized estimators, ridge regression