Applications of diversity measures and quasi U-Statistics

• Grant number: 11/15047-7
• Support Opportunities: Scholarships abroad - Research
• Start date: February 01, 2012
• End date: June 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Hildete Prisco Pinheiro
• Grantee: Hildete Prisco 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

The class of quasi U-statistics (Pinheiro et al., 2009; 2010) is constituted by a great variety of weighted U-statistics. Pinheiro et al. (2009) proves that the tests statistics for homogeneity among groups have assymptotically normal distributions, under the null hypothesis as well as under alternative ones (local or not). Pinheiro at al. (2005; 2011) present details about the applicability of one these test statistics based on generalized Hamming distances. The necessary regularity conditions for asymptotic normality are not very restrictive and concentrated on the weights of the weighted U-statistics. Therefore, it is possible to use quasi U-statistics in many applications. In applications to educational data, we want to use more robust methods to evaluate the differences with respect to the performance of students (Maiaet al., 2009). We consider a measure of diversity based on the relative rank gain of each student during his/her undergraduate studies. Other robust measures of diversities will also be considered. The second goal of this project is the development of new homogeneity tests for genomic data adapted to more realistic situations. (AU)

Scientific publications

(5)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MAIA, RAFAEL PIMENTEL; PINHEIRO, HILDETE PRISCO; PINHEIRO, ALUISIO. Academic performance of students from entrance to graduation via quasi U-statistics: a study at a Brazilian research university. Journal of Applied Statistics, v. 43, n. 1, SI, p. 72-86, JAN 2 2016. (13/00506-1, 11/15047-7)

PINHEIRO, HILDETE P.; SEN, PRANAB K.; PINHEIRO, ALUISIO; KIIHL, SAMARA F.. A nonparametric approach to assess undergraduate performance. STATISTICA NEERLANDICA, AUG 2020. (11/15047-7, 13/09357-9, 18/04654-9)

PINHEIRO, HILDETE P.; MAIA, RAFAEL P.; LIMA NETO, EUFRASIO A.; RODRIGUES-MOTTA, MARIANA. Zero-one augmented beta and zero-inflated discrete models with heterogeneous dispersion for the analysis of student academic performance. Statistical Methods and Applications, v. 28, n. 4, p. 749-767, DEC 2019. (14/03043-5, 11/15047-7)

PINHEIRO, HILDETE P.; SEN, PRANAB K.; PINHEIRO, ALUISIO; KIIHL, SAMARA F.. A nonparametric approach to assess undergraduate performance. STATISTICA NEERLANDICA, v. 74, n. 4, p. 21-pg., 2020-08-12. (13/09357-9, 11/15047-7, 18/04654-9)

MAIA, RAFAEL PIMENTEL; PINHEIRO, HILDETE PRISCO; PINHEIRO, ALUISIO. Academic performance of students from entrance to graduation via quasi U-statistics: a study at a Brazilian research university. Journal of Applied Statistics, v. 43, n. 1, p. 15-pg., 2016-01-02. (11/15047-7, 13/00506-1)