Merging Gini’s Indices under Quadratic Loss
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The Gini index is perhaps one of the most used indicators of economic and social condition. This article develops simultaneous estimation strategies of the Gini indices when samples are taken from several sources. In particular, we propose large sample test statistics for homogeneity of the indices. The null and non-null distributions of the proposed test statistics are derived. Further, a shrinkage estimator is suggested. The asymptotic bias and risk of the proposed estimator is derived and compared with benchmark estimator.
Keywords: Gini index, testing, shrinkage estimation, local alternatives, asymptotic quadratic risk. Back coverS. E. Ahmed, Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, CANADA N9B 3P4(e-mail:ahmed@uwindsor.ca).R. Ghori, Department Mathematics & Statistics, University of Prince Edward Island, Canada (rghori@upei.ca). M. N. Goria, Dipartimento di Informatica e Studi Aziendali, via Inama, 5, I-38100 Trento, TN, Italy (e-mail: mohammed.nawazgoria@economia.unitn.it). A. Hussein, Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, CANADA N9B 3P4(e-mail: hussein@uwindsor.ca).
S. E. Ahmed, Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, CANADA N9B 3P4(e-mail:ahmed@uwindsor.ca).
R. Ghori, Department Mathematics & Statistics, University of Prince Edward Island, Canada (rghori@upei.ca). M. N. Goria, Dipartimento di Informatica e Studi Aziendali, via Inama, 5, I-38100 Trento, TN, Italy (e-mail: mohammed.nawazgoria@economia.unitn.it). A. Hussein, Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, CANADA N9B 3P4(e-mail: hussein@uwindsor.ca). |
