Title: Simultaneous confidence bands for ratios of quantile functions and growth incidence curves
Authors: Fabian Dunker - University of Canterbury (New Zealand) [presenting]
Tatyana Krivobokova - Georg-August-Universitaet Goettingen (Germany)
Stephan Klasen - University of Goettingen (Germany)
Abstract: Ratios of quantile functions are an important tool to evaluate the distributional pattern of growth processes when repeated cross-sectional data are available. The most popular example are Growth Incidence Curves (GIC) that allow assessments whether income growth in developing countries has been pro-poor. Such assessments depend on the location and slope of the growth incidence curve as well as the confidence bands surrounding the curve. We present a construction of uniform confidence bands for GICs and similar ratios of quantile functions. In contrast to existing point-wise confidence bands that are created via bootstrapping, the bands we propose are valid simultaneously for almost all points in the domain of the quantile functions and GICs. They allow for an assessment of the location and on larger scales of the slope of the curves. Furthermore, the construction does not depend on bootstrapping but on an analysis of the asymptotic distribution of GICs. This allows for significantly faster algorithms. The performance of the confidence band is demonstrated in simulations and in an example using income data from Uganda for 1999-2005.