Asymptotic linearity and limit distributions, approximations.

• Autor(a) principal: Mexia, J.T., Oliveira, M.M.
• Data de Publicação: 2010
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/2594
• topic: Asymptotic linearity

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 m þ X, with X any random vector and m non-random vector with JmJ-þ1. This class contain the polynomials in m þ 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.