Abstract: We consider estimating the finite population proportion of a fixed number of mutually exclusive and exhaustive categories from survey responses obtained by probability sampling. The customary design-based estimator does not make use of the auxiliary data available for all the population units at the estimation stage. We adopt a model-based predictive approach to incorporate this information. In the first part of our paper we consider a parametric generalization of multinomial logit model for prediction of non-sampled responses which is then used to obtain the estimates of proportions. The asymptotic bias and variance of these estimators are obtained. The main drawback of this approach is, being a parametric model it may suffer from model misspecification and thus, may sometimes produce estimates that may perform worse than the usual design-based estimates. To overcome this drawback, in the next part of this paper we replace the multinomial logit type model by a nonparametric model using recently developed random coefficients splines models. Finally, we carry out a simulation study. It shows that the nonparmetric approach may lead to an appreciable improvement over both parametric and design-based approaches when the regression function is quite different from multinomial logit.

(A joint work with Sumanta Adhya and Gaurangadeb Chattopadhyay, Calcutta University, India)