Around 1979, Anil Bera and Carlos Jarque while working on their dissertations on regression analysis, have applied the Lagrange multiplier principle to the Pearson family of distributions to test the normality of unobserved regression residuals and found that the JB test was asymptotically optimal (although the sample size needed to “reach” the asymptotic level was quite large).
Carlos Jarque, Secretary General of the Inter-American Development Bank, Washington DC, former President of INEGI in Mexico, former President of the Statistical Commission of the UN and Minister of Social Development in the Cabinet of Ernesto Zedillo
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