Duchesne, Pierre and Francq, Christian (2010): On testing for the mean vector of a multivariate distribution with generalized and {2}inverses.

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Abstract
Generalized Wald's method constructs testing procedures having chisquared limiting distributions from test statistics having singular normal limiting distributions by use of generalized inverses. In this article, the use of twoinverses for that problem is investigated, in order to propose new test statistics with convenient asymptotic chisquare distributions. Alternatively, Imhofbased test statistics can also be defined, which converge in distribution to weighted sum of chisquare variables; The critical values of such procedures can be found using Imhof's (1961) algorithm. The asymptotic distributions of the test statistics under the null and alternative hypotheses are discussed. Under fixed and local alternatives, the asymptotic powers are compared theoretically. Simulation studies are also performed to compare the exact powers of the test statistics in finite samples. A data analysis on the temperature and precipitation variability in the European Alps illustrates the proposed methods.
Item Type:  MPRA Paper 

Original Title:  On testing for the mean vector of a multivariate distribution with generalized and {2}inverses 
Language:  English 
Keywords:  twoinverses; generalized Wald's method; generalized inverses; multivariate analysis; singular normal distribution 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General 
Item ID:  19740 
Depositing User:  Christian Francq 
Date Deposited:  07. Jan 2010 08:34 
Last Modified:  25. Feb 2013 09:50 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/19740 