Abstract
This note establishes the weak laws of large numbers with general normalizing sequences for weighted sums of dependent identically distributed random vectors taking values in real separable Hilbert spaces. The dependent structures include pairwise and coordinatewise negative dependence and coordinatewise negative association. The sharpness of the result for the case where the random vectors are coordinatewise negatively associated is illustrated by an example.
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Acknowledgements
The authors are grateful to Dr. Le Van Thanh (Vinh University, Viet Nam) for his valuable comments. Especially, the authors would like to thank two referees for constructive, perceptive, and substantial comments and suggestions which enabled us to greatly improve the paper.
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Anh, V.T.N., Hien, N.T.T. On the weak laws of large numbers for weighted sums of dependent identically distributed random vectors in Hilbert spaces. Rend. Circ. Mat. Palermo, II. Ser 70, 1245–1256 (2021). https://doi.org/10.1007/s12215-020-00555-w
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DOI: https://doi.org/10.1007/s12215-020-00555-w
Keywords
- Identically distributed
- Pairwise and coordinatewise negative dependence
- Coordinatewise negatively associated
- Hilbert space
- Slowly varying function