| Grant number: | 08/09286-6 |
| Support Opportunities: | Scholarships abroad - Research |
| Start date: | January 19, 2009 |
| End date: | February 07, 2009 |
| Field of knowledge: | Physical Sciences and Mathematics - Probability and Statistics - Statistics |
| Principal Investigator: | Aluísio de Souza Pinheiro |
| Grantee: | Aluísio de Souza Pinheiro |
| Host Investigator: | Pranab Kumar Sen |
| Host Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
| Institution abroad: | University of North Carolina at Chapel Hill (UNC), United States |
Abstract In several applications, information is drawn from qualitative variables. In such cases, measures of central tendency and dispersion are rarely appropriate. Variability for categorical data can be correctly quantified by the so-called diversity measures. These measures can be modified to quantify heterogeneity between groups (or subpopulations). Pinheiro et al. (2005) shows that Hamming distance can be employed in such way and the resulting estimator of heterogeneity between populations will be asymptotically normal under mild conditions. Pinheiro et al. (2006) proposes a class of degree 2 kernels for which a class of weighed $U$-statistics, quasi U-statistics is asymptotically normal, under suitable regularity conditions. Sen et al. (2007) extends this class to degree M kernels. We propose to use this powerful tool to study the asymptotic behavior of a collection of transformed classic diversity measures. With this, we will be able to estimate them in a similar way instead of the usual individual estimation procedures. We will also study under which conditions asymptotic normality will hold. (AU) | |
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