Exact Critical Values for Mood's Distribution-Free Test Statistic for Dispersion and Its Normal Approximation

Technometrics ◽  
1968 ◽  
Vol 10 (3) ◽  
pp. 497-507 ◽  
Author(s):  
Nico F. Laubscher ◽  
F. E. Steffens ◽  
Elsie M. De Lange
Keyword(s):  
Normal Approximation ◽  
Critical Values ◽  
Test Statistic ◽  
Distribution Free

Testing for individual sphericity in heterogeneous panels

Biometrika ◽  
2019 ◽  
Vol 106 (3) ◽  
pp. 740-747
Author(s):  
Simon A Broda
Keyword(s):  
Distribution Function ◽  
Normal Approximation ◽  
Empirical Work ◽  
Null Distribution ◽  
Saddlepoint Approximation ◽  
Test Statistic ◽  
Cross Sectional ◽  
P Values ◽  
Cross Sectional Dimension ◽  
Heterogeneous Panels

Summary This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.

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