scholarly journals Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality

2002 ◽  
Vol 32 (1) ◽  
pp. 17-50 ◽  
Author(s):  
Hirofumi Wakaki ◽  
Hirokazu Yanagihara ◽  
Yasunori Fujikoshi
Keyword(s):  
Asymptotic Expansions ◽  
Linear Hypothesis ◽  
Test Statistics ◽  
Null Distributions ◽  
Distributions Of Test Statistics

Higher-Order Approximations to the Null Distributions of Test Statistics for Nonlinear Restrictions on Regression Coefficients

1988 ◽  
Vol 4 (2) ◽  
pp. 275-299
Author(s):  
Kimio Morimune
Keyword(s):  
Asymptotic Expansions ◽  
Simultaneous Equations ◽  
Regression Coefficients ◽  
Test Statistics ◽  
Lagrange Multiplier Test ◽  
Null Distributions ◽  
Asymptotic Size ◽  
Simultaneous Equations Models ◽  
Real Size ◽  
Special Case

Asymptotic expansions of the distributions of likelihood ratio and Lagrange multiplier test statistics for nonlinear restrictions on regression coefficients are derived under the null hypothesis. Nonlinear restrictions include, as a special case, the identifiability restrictions in the simultaneous equations models. Our analyses of simultaneous equations deal not only with single equations but also subsystems and complete systems. The asymptotic expansions we derive are informative about deviations of the real size of test from the nominal asymptotic size.

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