Chi-Square Goodness-of-Fit Tests Based on Dependent Observations

  • Kamal C. Chanda
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)


An attempt has been made in this article to investigate the sampling properties of standard goodness-of-fit chi-square tests based on interdependent observations which are obtained from a strictly stationary and strong-mixing random process. We conclude that the null distributions of the test statistics are largely determined by the multivariate probability structure of the process. A few examples are used to illustrate this point.

Key Words

goodness-of-fit tests chi-square tests strictly stationary and strong mixing processes linear processes 


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  1. Bartlett, M.S. (1950). The frequency goodness-of-fit test for probability chains. Proceedings of the Cambridge Philosophical Society, 47, 86–95.MathSciNetCrossRefGoogle Scholar
  2. Chanda, K.C. (1974). Strong mixing properties of linear stochastic processes. Journal of Applied Probability, 11, 401–408.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Chanda, K.C. (1976). Some comments on sample quantiles for dependent observations. Communications in Statistics - Theory and Methods, A5 (14), 1385–1392.MathSciNetCrossRefGoogle Scholar
  4. Chernoff, H., Lehmann, E.L. (1954). The use of maximum likelihood estimates in x2 tests for goodness-of-fit. Annals of Mathematical Statistics, 25, 579–586.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Cramer, H. (1946). Mathematical Methods of Statistics. Princeton University Press, Princeton.zbMATHGoogle Scholar
  6. Dutta, K., Sen, P.K. (1971). On the Bahadur representation of sample quantiles in some stationary multivariate auto- regressive processes. Journal of Multivariate Analysis, 1, 186–198.MathSciNetCrossRefGoogle Scholar
  7. Graybill, F.A. (1976). Theory and Applications of the Linear Model. Duxbury Press, North Scituate, Massachusetts.Google Scholar
  8. Gorodetskii, V.V. (1977). On the strong mixing property for linear sequences. Theory of Probability and its Applications, 22, 411–413.CrossRefGoogle Scholar
  9. Patankar, V.N. (1954). The goodness-of-fit of frequency distributions obtained from stochastic processes. Biometrika, 50, 450–462.MathSciNetGoogle Scholar
  10. Rozanov, Yu. A. (1967). Stationary Random Processes. Holden- Day, San Francisco.zbMATHGoogle Scholar
  11. Watson, G.S. (1959). Some recent results in chi-square goodness-of-fit tests. Biometrics, 15, 440–468.zbMATHCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Kamal C. Chanda
    • 1
  1. 1.Department of MathematicsTexas Tech UniversityLubbockUSA

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