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Concentration inequalities and limit theorems for randomized sums

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Abstract.

Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals.

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Author information

Correspondence to Sergey G. Bobkov.

Additional information

Research supported in part by NSF Gr. No. 0405587

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Bobkov, S., Götze, F. Concentration inequalities and limit theorems for randomized sums. Probab. Theory Relat. Fields 137, 49–81 (2007). https://doi.org/10.1007/s00440-006-0500-9

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Key words or phrases

  • Concentration
  • typical distributions
  • central limit theorem
  • selfnormalized statistics
  • orthogonal polynomials
  • pairwise independent random variables