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.