Asymptotic linearity and limit distributions,approximations |
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Authors: | Joã o T. Mexia,Manuela M. Oliveira |
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Affiliation: | 1. FCT Nova University of Lisbon, Department of Mathematics, Quinta da Torre, 2825 Monte da Caparica, Portugal;2. University of Èvora, Department of Mathematics and CIMA – Center for Research on Mathematics and its Applications, Colégio Luís António Verney, Rua Romão Ramalho 59, 7000-671 Évora, Portugal |
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Abstract: | Linear and quadratic forms as well as other low degree polynomials play an important role in statistical inference. Asymptotic results and limit distributions are obtained for a class of statistics depending on μ+X, with X any random vector and μ non-random vector with ∥μ∥→+∞. This class contain the polynomials in μ+X. An application to the case of normal X is presented. This application includes a new central limit theorem which is connected with the increase of non-centrality for samples of fixed size. Moreover upper bounds for the suprema of the differences between exact and approximate distributions and their quantiles are obtained. |
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Keywords: | Asymptotic linearity Linear and quadratic forms Polynomials Normal distributions Central limit theorems |
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