On asymptotic non-normality of null distributions of mrpp statistics

Abstract

Severe departures from normality occur frequently for null distributions of statistics associated with applications of mulLi-response permutation procedures (MRPP) for either small or large finite populations. This paper describes the commonly encountered situation associated with asymptotic non-normality for null distributions of MRPP statistics which does not depend on the underlying multivariate distribution. In addition, this paper establishes the existence of a non-degenerate underlying distribution for which the null distributions of MRPP statistics are asymptotically non-normal for essentially all size structure configurations. It is known that MRPP statistics are symmetric versions of a broader class of statistics, most of which are asymmetric. Because of the non-normality associated with null distributions of MRPP statistics, this paper includes necessary results for inferences based on the exact first three moments of anv statistic in this broader class (analogous to existing results for MRPP statistics).

Keywords

StatisticsAsymptotic distributionNull (SQL)NormalityMathematicsPermutation (music)Distribution (mathematics)Class (philosophy)EconometricsEstimatorPhysicsMathematical analysisComputer scienceArtificial intelligence

Affiliated Institutions

Colorado State University US

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Publication Info

Year: 1979
Type: article
Volume: 8
Issue: 15
Pages: 1541-1550
Citations: 104
Access: Closed

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APA Style

                            
                                    Paul W. Mielke
                                
                            (1979). 
                            On asymptotic non-normality of null distributions of mrpp statistics. 
                            Communication in Statistics- Theory and Methods
                            , 8
                            (15)
                            , 1541-1550.
                            https://doi.org/10.1080/03610927908827850

Identifiers

DOI: 10.1080/03610927908827850