Using the compactness in large deviation theory, this note describes a large deviation upper bound by a lower semicontinuous function. It then obtains a characterization for exponential convergence and discusses exponential convergence rates.
Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of
β Scribed by Guodong Xing; Shanchao Yang
- Publisher
- Springer US
- Year
- 2009
- Tongue
- English
- Weight
- 503 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0894-9840
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let [X n , n 1] be a sequence of stationary negatively associated random variables, Under some suitable conditions, the central limit theorem and the weak convergence for sums are investigated. Applications to limiting distributions of estimators of Var S n are also discussed.
We discuss complete convergence for weighted sums of negatively associated (NA) random variables. The result on i.i.d. case of Li et al. (J. Theoret. Probab. 8 (1995) 49 -76) is generalized and extended. Also, Gut's (Probab. Theory Related Fields 97 (1993) 169 -178) result on CesΓ aro summation of i
is non-decreasing. Thus, if one applies the c,-inequality, the inequality follows trivially. From this and from the preceding inequality we obtain By our condition the sums on the right hand side converge to 0 as n -+ + 00. This proves the assertion. Remarks. It is easy to see that for p > 2 our c