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A remark on the connection between the large deviation principle and the central limit theorem

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  • Bryc, Wlodzimierz

Abstract

We point out that under a suitable regularity condition the central limit theorem can be obtained as a consequence of the large deviation principle.

Suggested Citation

  • Bryc, Wlodzimierz, 1993. "A remark on the connection between the large deviation principle and the central limit theorem," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 253-256, November.
    • Handle: RePEc:eee:stapro:v:18:y:1993:i:4:p:253-256
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    Citations

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    Cited by:

    1. Federico Camerlenghi & Claudio Macci & Elena Villa, 2021. "Asymptotic behavior of mean density estimators based on a single observation: the Boolean model case," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 1011-1035, October.
    2. Pakdaman, Khashayar & Thieullen, Michèle & Wainrib, Gilles, 2012. "Asymptotic expansion and central limit theorem for multiscale piecewise-deterministic Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2292-2318.
    3. Camilla Calì & Maria Longobardi & Claudio Macci & Barbara Pacchiarotti, 2022. "Asymptotic results for linear combinations of spacings generated by i.i.d. exponential random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 733-752, August.
    4. Włodzimierz Bryc & Amir Dembo, 1997. "Large Deviations for Quadratic Functionals of Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 10(2), pages 307-332, April.
    5. Beghin, Luisa & Macci, Claudio, 2017. "Asymptotic results for a multivariate version of the alternative fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 260-268.

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