THE GROUPING PROBLEM IN DISTRIBUTION-FREE PLANAR REGRESSION

In the planar regression model having two slope parameters and identically distributed errors, exact distribution-free inference about one parameter may be carried out by grouping the observations, eliminating the nuisance parameter and reducing the model to simple linear regression, allowing exact distribution-free methods for slope to be employed. This model reduction involves a loss of efficiency: the choice of an optimal grouping to minimize efficiency loss is discussed.