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Abstract

Generalized Wald-s method constructs testing procedures having chi-squared limiting distributionsfrom test statistics having singular normal limiting distributions by use of generalized inverses.In this article, the use of two-inverses for that problem is investigated,in order to propose new test statistics with convenient asymptotic chi-square distributions.Alternatively, Imhof-based test statistics can also be defined, which convergein distribution to weighted sum of chi-square variables; The critical values of such procedures can be foundusing 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 illustratesthe 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: two-inverses; 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-





Author: Duchesne, Pierre

Source: https://mpra.ub.uni-muenchen.de/19740/







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