期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2005
卷号：67
期号：02
出版社：Indian Statistical Institute
摘要：The concept of Fractile Graphical Analysis (FGA) was introduced by Prasanta Chandra Mahalanobis (see Mahalanobis, 1960). It is one of the earliest nonparametric regression techniques to compare two regression functions for two bivariate populations $(X,Y)$. This method is particularly useful for comparing two regression functions where the covariate ($X$) for the two populations are not necessarily on comparable scales. For instance, in econometric studies, the prices of commodities and people's incomes observed at different time points may not be on comparable scales due to inflation. In this paper, we consider a smooth estimate of the fractile regression function and study its statistical properties. We prove the consistency and asymptotic normality of the estimated fractile regression function defined through general weight functions. We also investigate some procedures based on the idea of resampling to test the equality of the fractile regression functions for two different populations. These methods are applied to some real data sets obtained from the Reserve Bank of India, and this leads to some interesting and useful observations. In course of our investigation, we review many of Mahalanobis' original ideas relating to FGA {\it vis a vis} some of the key ideas used in nonparametric kernel regression.
