Asymptotic linearity and limit distributions, approximations

作者：Mexia Joao T; Oliveira Manuela M^*

来源：Journal of Statistical Planning and Inference, 2010, 140(2): 353-357.

DOI：10.1016/j.jspi.2009.09.014

• Asymptotic linearity
• Linear and quadratic forms
• Polynomials
• Normal distributions
• Central limit theorems

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 mu + X, with X any random vector and mu non-random vector with parallel to mu parallel to -> + infinity. This class contain the polynomials in mu + 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.

• 出版日期2010-2