Abstract
The tail probability inequalities for the sum of independent unbounded random variables on a probability space (Ω, T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Ω, T, P). The probability exponential inequalities for sums of independent unbounded random variables were given. As applications of the results, some interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables.
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References
Bennett G. Probability inequalities for the sum of independent random variables [J]. Journal of the American Statistical Association, 1962,57(1):33–45.
Hoeffding W. Probability inequalities for sums of bounded random variables [J]. JASA, 1963,58(1): 13–30.
Uspensky J V. Introduction to Mathematical Probability [M]. New York: McGraw Hill, 1937.
Pollard D. Convergence of Stochastic Processes [M], New York: Springer-Verlag, 1984.
Dudley R M. A Course on Empirical Processes, Springer Lecture Notes in Mathematics [M], 1097, New York: Springer-Verlag, 1984.
Shorack G R, Wellner J A. Empirical Processes With Applications to Statistics [M]. New York: Wiley, 1986.
Chow Y S, Teicher H. Probability Theory [M]. New York: Springer-Verlag, 1988.
Stout W F. Almost Sure Convergence [M]. New York: Academic Press, Inc, 1974.
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Zhang, Dx., Wang, Zc. Probability Inequalities for Sums of Independent Unbounded Random Variables. Applied Mathematics and Mechanics 22, 597–601 (2001). https://doi.org/10.1023/A:1016352608299
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DOI: https://doi.org/10.1023/A:1016352608299