Asymptotic efficiency of rank tests of randomness against autocorrelation

  • R. J. Aiyar


This note is concerned with the problem of testing the hypothesisH of randomness against the alternative that the variables are auto-correlated. Two rank tests ofH are considered and their asymptotic efficiencies relative to the classical normal theory tests are obtained.


Asymptotic Normality Finite Variance Asymptotic Efficiency Continuous Distribution Function Maximum Likelihood Esti 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Anderson, T. W. (1959). On asymptotic distributions of estimates of parameters of stochastic difference equations,Ann. Math. Statist.,30, 676–687.MATHMathSciNetGoogle Scholar
  2. [2]
    Chernoff, H. and Savage, I. R. (1958). Asymptotic normality and efficiency of certain non-parametric test statistics,Ann. Math. Statist.,29, 972–994.MathSciNetGoogle Scholar
  3. [3]
    Diananda, P. H. (1953). Some probability limit theorems with statistical applications,Proc. Camb. Phil. Soc.,49, 239–246.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Jogdeo, K. (1968). Asymptotic normality in non-parametric methods,Ann. Math. Statist.,39, 905–922.MATHMathSciNetGoogle Scholar
  5. [5]
    LeCam, L. (1960). Locally asymptotically normal families of distributions,Univ. Calif. Pub. Statist.,3, 37–98.MATHMathSciNetGoogle Scholar
  6. [6]
    Noether, G. E. (1955). On a theorem of Pitman,Ann. Math. Statist.,26, 64–68.MATHMathSciNetGoogle Scholar
  7. [7]
    Wald, A. and Wolfowitz, J. (1943). An exact test of randomness in the non-parametric case based on serial correlation,Ann. Math. Statist.,14, 378–388.MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1981

Authors and Affiliations

  • R. J. Aiyar
    • 1
  1. 1.San Francisco State UniversitySan FranciscoUSA

Personalised recommendations