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Bikas Sinha, Indian Statistical Institute

### De La Garza Phenomenon Re-visited

De La Garza [ AMS (1954 ) ] made a pertinent observation in the
context of polynomial regression under homoscedastic errors. With one
non-stochastic covariate in a p-th degree polynomial regression based
on n observations ( at least p + 1 being distinct ), he demonstrated
that the same amount of information on the regression parameters can
be obtained by restricting to a suitably chosen set of EXACTLY p + 1
observations with suitable "weights".

In this talk we present various results on optimal regression
designs, properly exploiting the above phenomenon.

We also present some results in the context of a linear
regression under heteroscedastic errors.