Fabian Dunker, Stephan Klasen, Tatyana Krivobokova
arXiv 24 Oct 2017 · Statistics — Methodology · publishedElectronic Journal of Statistics (2019) · 2 citations (OpenAlex)
arXiv:1710.09009 · PDF · DOI · OpenAlex · Extracted main text
Ratio of medians or other suitable quantiles of two distributions is widely used in medical research to compare treatment and control groups or in economics to compare various economic variables when repeated cross-sectional data are available. Inspired by the so-called growth incidence curves introduced in poverty research, we argue that the ratio of quantile functions is a more appropriate and informative tool to compare two distributions. We present an estimator for the ratio of quantile functions and develop corresponding simultaneous confidence bands, which allow to assess significance of certain features of the quantile functions ratio. Derived simultaneous confidence bands rely on the asymptotic distribution of the quantile functions ratio and do not require re-sampling techniques. The performance of the simultaneous confidence bands is demonstrated in simulations. Analysis of the expenditure data from Uganda in years 1999, 2002 and 2005 illustrates the relevance of our approach.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cheng, C. and Wu, J (2010) Interval estimation of quantile ratios applied to anti-cancer drug screening by xenograft experiments | 0.811 | 4 | 2 | 100% |
| 2 | Csörgo, M. and Révész, P (1984) Two approaches to constructing simultaneous confidence bounds for quantiles | 0.737 | 3 | 3 | 67% |
| 3 | Dominici, F., Cope, L., Naiman, D. Q., and Zeger, S. L (2005) Smooth quantile ratio estimation | 0.644 | 4 | 1 | 100% |
| 4 | Csörgo, M (1983) Quantile processes with statistical applications, volume 42 of CBMS-NSF Regional Conference Series in Applied Mathematics | 0.511 | 4 | 2 | 25% |
| 5 | Klasen, S (2008) Economic growth and poverty reduction: Measurement issues using income and non-income indicators self | 0.511 | 2 | 1 | 100% |
| 6 | Bourguignon, F (2011) Non-anonymous growth incidence curves, income mobility and social welfare dominance | 0.405 | 1 | 1 | 100% |
| 7 | Chesneau, C., Dewan, I., and Doosti, H (2016) Nonparametric estimation of a quantile density function by wavelet methods | 0.405 | 1 | 1 | 100% |
| 8 | Csörgo, M., Horváth, L., and Deheuvels, P (1991) Estimating the quantile-density function | 0.405 | 1 | 1 | 100% |
| 9 | Csörgo, M. and Révész, P (1978) Strong approximations of the quantile process | 0.405 | 1 | 1 | 100% |
| 10 | Cantelli, F. P (1933) Sulla determinazione empirica delle leggi di probabilita | 0.405 | 1 | 1 | 100% |
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