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• W1566332670 abstract "Fractile Graphical Analysis was proposed by Prashanta Chandra Mahalanobis (Mahalanobis, 1960) in a series of papers and seminars as a method for comparing two distributions controlling for the rank of a covariate through groups. Mahalanobis used a heuristic method of approximating the standard error of the dependent variable using graphs from two independently selected subsamples. We revisit the technique of graphical analysis with some historical perspectives. We a propose a new non-parametric regression method called Fractile Regression where we condition on the ranks of the covariate, and compare it with existing regression techniques. We apply this method to predict mutual fund in‡ow distributions after conditioning on returns and to wage distribution after conditioning for educational quali…cations. Finally, we investigate large and …nite sample properties of regression coe¢ cients both analytically and through Monte Carlo simulations. JEL Classi…cation: C12, C14, C52 Keywords: Non-parametric regression, distribution comparison, Fractile Graphical Analysis, rank regression, quantile regression, Gini coe¢ cient, concentration curves, simulation methods, mutual fund in‡ow 1 Motivation and Background Fractile Graphical Analysis was proposed by Prashanta Chandra Mahalanobis (Mahalanobis, 1961) in a series of papers and seminars as a method to take into account the e¤ect of a covariate while comparing two distributions. Unlike the parametric method of linear least squares regression analysis Mahalanobis proposed a more non-parametric way of controlling the covariates (possibly, more than one) using the ranks of fractile groups (possibly unequal). The method provides a graphical tool for comparing both complete distributions of the variable of interest (like income or expenditure) for all values of the covariate as well as speci…c fractiles. Mahalanobis used a visual method of approximating the standard error of the income at all the fractiles of the covariate for the same graph by taking two independently selected and obtaining a graph for each of the subsamples besides the combined sample. The method proposed by Mahalanobis for estimating the error area of a graph was later hailed as a precursor to the genesis of latter day bootstrap methodology (Efron 1979a,b; Hall, 2003). FGA can used to test whether two distributions of the graphs of two populations are di¤erent by looking at the Area of Separation between the two graphs. It is worth mentioning that the graphs are a more general version of the Lorenz concentration curve and more speci…c concentration curves where we look at the cumulative relative sums of the levels of the variable of interest (for example expenditure or income) in place of the actual values. Hence, FGA can be used to compare the error in estimating Lorenz curves or speci…c concentration curves. The main contribution of the Fractile Graphical Analysis were twofold, …rst it provided a method of using interpenetrating network of subsamples to estimate the error region and perform a simple graphical test of the whole or a range of values of the fractiles where the distributions are di¤erent (see the discussion in Swami, 1963 and Iyengar and Bhattacharya, 1965). The point raised in Swami(1963) that FGA was a novel way of looking at the age-old problem of concentration curves and Gini Coe¢ cient is also misleading as FGA provides a method of comparison" @default.
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• W1566332670 date "2005-01-01" @default.
• W1566332670 modified "2023-09-27" @default.
• W1566332670 title "Fractile Regression and Its Applications in Economics and Finance" @default.
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