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Asymptotic representations of self-normalized sums
Asymptotic representations self-normalized sums
2009/9/23
Asymptotic representations of self-normalized sums。
Acknowledgment of Priority: When Does a Randomly Weighted Self-normalized Sum Converge in Distribution? (Elect. Comm. in Probab. 10 (2005), 70--81)
Domain of attraction selfCnormalize sums regular variation
2009/4/27
Christian Houdre has kindly pointed us to a paper by A. Fuks, A. Joffe and J. Teugels, where their Theorem 5.3 is our Proposition 3 in the case 0
When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?
Domain of attraction selfCnormalize sums regular variation
2009/4/24
We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize...
When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?
Weighted Self-normalized Sum Distribution
2009/4/7
We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize...
Exponential bounds for multivariate self-normalized sums
non-parametric framework self-normalized sums random variables
2009/3/23
In a non-parametric framework, we establish some non-asymptotic bounds for self-normalized sums and quadratic forms in the multivariate case for symmetric and general random variables. This bounds are...
Exponential inequalities for self-normalized martingales with applications
Exponential inequalities martingales autoregressive processes branching processes
2010/4/30
We propose several exponential inequalities for self-normalized
martingales similar to those established by De la Pe˜na. The keystone
is the introduction of a new notion of random variable heav...