A Note on Convergence to Mixtures of Normal Distributions,
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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Double arrays of random variables obtained by normalizing a sequence that is asymptotically close to a martingale difference sequence are considered, and conditions ensuring that the row sums converge in distribution to a mixture of normal distributions are found. The main condition is that the sums of squares in each row converge in probability to a random variable.
- Statistics and Probability