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The limit distributions of likelihood ratio and cumulative sum tests for a change in a binomial probability

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  • Horváth, Lajos

Abstract

We obtain limit theorems for likelihood ratio and cumulative sums tests. In the case of the likelihood ratio the centralising and normalising sequences go to infinity and the limit is the Gumbel (double exponential) distribution. The first and the last few observations determine the limit, which also explains why the likelihood ratio test is very powerful on the tails.

Suggested Citation

  • Horváth, Lajos, 1989. "The limit distributions of likelihood ratio and cumulative sum tests for a change in a binomial probability," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 148-159, October.
  • Handle: RePEc:eee:jmvana:v:31:y:1989:i:1:p:148-159
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    References listed on IDEAS

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    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, pages 135-156.
    3. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
    4. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
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    Cited by:

    1. Baron, Michael & Rukhin, Andrew L., 2001. "Perpetuities and asymptotic change-point analysis," Statistics & Probability Letters, Elsevier, pages 29-38.

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