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Limiting values of large deviation probabilities of quadratic statistics

Author

Listed:
  • Jeurnink, G. A. M.
  • Kallenberg, W. C. M.

Abstract

Application of exact Bahadur efficiencies in testing theory or exact inaccuracy rates in estimation theory needs evaluation of large deviation probabilities. Because of the complexity of the expressions, frequently a local limit of the nonlocal measure is considered. Local limits of large deviation probabilities of general quadratic statistics are obtained by relating them to large deviation probabilities of sums of k-dimensional random vectors. The results are applied, e.g., to generalized Cramér-von Mises statistics, including the Anderson-Darling statistic, Neyman's smooth tests, and likelihood ratio tests.

Suggested Citation

  • Jeurnink, G. A. M. & Kallenberg, W. C. M., 1990. "Limiting values of large deviation probabilities of quadratic statistics," Journal of Multivariate Analysis, Elsevier, vol. 35(2), pages 168-185, November.
    • Handle: RePEc:eee:jmvana:v:35:y:1990:i:2:p:168-185
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