The conventional approach has many drawbacks. Follain and Jimenez [1985]discussed many of those in detail. One of which I try to address in this paper is the functional form "pre-selection". As pointed out in the last paragraph, researchers often specify, in one way or another, specific functional forms that embody assumptions about the references of households. This renders researchers much discretion on the underlying relationships that are under studying.
A better approach would be to use nonparametric estimation approach in both stages so as to avoid those unnecessary errors in functional form selection. By nonparametric
estimation, it means that the underlying functional relationship is estimated without ex ante functional form selection. A "double nonparametric" approach to estimate the demand structures has been proposed by Mr. Stephen Sheppard. It is the second order objective of this paper to pursue his proposed "double nonparametric" approach.
Following Mr. Sheppard's suggestion, the first stage involves applying nonparametric Kernel regression method, which will be discussed later, to estimate the
characteristic or marginal prices for observed housing and neighborhood characteristics from a hedonic price function. The second stage uses estimation technique developed by
Varian [1982, '85, '90 and '93] to estimated the demand structures nonparametrically.