Strong Large Deviations Theorems for the Ratio of the Independent Random Variables

  • Cho, Dae-Hyeon (Department of Statistics, Inje University, KimHae 621-170) ;
  • Jeon, Jong-Woo (Department of Computer Science and Statistics, Seoul National University, Seoul 151-742)
  • Published : 1994.12.01

Abstract

In this paper, we prove a strong large deviations theorem for the ratio of independent randoem variables with error rate of $O(n^{-1})$. To obtain our results we use the inversion formula for the tail probability and apply the Chaganty and Sethuraman's (1985) approach.

Keywords

References

  1. Annals of Mathematical Statistics v.31 On deviation of the sample mean Bahadur,R.R.;Ranga Rao,R.
  2. The Annals of Probability v.7 Large deviations of the sample mean in general vector spaces Bahadur,R.R.;Zabel,S.L.
  3. The Annals of Probability v.13 Large deviation local limit theorems for arbitrary sequences of random variables Chaganty,N.R.;Sethuraman,J.
  4. Technical report Strong large deviation and local limit theorems Chaganty,N.R.;Sethuraman,J.
  5. Annals of Mathematical Statistics v.23 A mesure of asymptotic efficiency for tests of a hypothesis based sum of observation Chernoff,H.
  6. InJe Journal v.7 no.1 A large deviation local limit theorem for the ratio of independent sequences of random variables Cho,D.H.
  7. Journal of Korean Mathematical Society v.29 A strong large deviations theorem for the ratio of independent random variables Choi,H.S.;Kim,C.Y.;Kim,W.C.;Jeon,J.W.
  8. Actualites Scienfiques et Industrielles v.736 Sur un nouveau theoreme-limite de la theorie des probabilites Cramer,H.
  9. Annals of Mathematical Statistics v.40 On the probability of large deviations and exact slopes Sievers,G.L.
  10. The Annals of Probability v.6 no.5 Convergence rates of large deviation probabilities in the multidimentional case Steinebach,J.
  11. The Annals of Probability v.10 no.2 Cramer type deviations for linear combinations for order statistics Vandemaele,M.;Veraverbeke,N.