SOME LIMIT THEOREMS IN REGRESSION THEORY

SUMMARY. {X,Y) follows an unknown bivariate distribution with 0<JX<^1 and the regression of Y on X is continuous and a sequence of observations on (X,Y) are made. An estimate of the unknown regression function based on these observations and motivated by the method of Fractile Graphical Analysis has been suggested. Its large sample properties, viz., convergence in probability and almost sure uniform convergence to the true regression function have been investigated. Large sample tests for a specified regression function have also been proposed for the case when the conditional variance function of Y on X is known and for the case when it is unknown.