On the Le Cam distance between Poisson and Gaussian experiments and the asymptotic properties of Szasz estimators
- Creators
- Ouimet, Frédéric
Abstract
In this paper, we prove a local limit theorem for the ratio of the Poisson distribution to the Gaussian distribution with the same mean and variance, using only elementary methods (Taylor expansions and Stirling's formula). We then apply the result to derive an upper bound on the Le Cam distance between Poisson and Gaussian experiments, which gives a complete proof of the sketch provided in the unpublished set of lecture notes by Pollard [41], who uses a different approach. We also use the local limit theorem to derive the asymptotics of the variance for Bernstein c.d.f. and density estimators with Poisson weights on the positive half-line (also called Szasz estimators). The propagation of errors in the literature due to the incorrect estimate in Lemma 2 (iv) of Leblanc [32] is addressed in the Appendix.
Additional Information
© 2021 Elsevier Inc. Received 16 October 2020, Available online 4 February 2021. F. O. is supported by a postdoctoral fellowship from the NSERC (PDF) and FRQNT (B3X supplement). The author would like to thank an anonymous referee for his valuable comments that led to improvements in the presentation of this paper.Attached Files
Accepted Version - 2010.05146.pdf
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Additional details
- Alternative title
- A local limit theorem for the Poisson distribution and its application to the Le Cam distance between Poisson and Gaussian experiments and asymptotic properties of Szasz estimators
- Eprint ID
- 108599
- DOI
- 10.1016/j.jmaa.2021.125033
- Resolver ID
- CaltechAUTHORS:20210401-083400555
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Fonds de recherche du Québec – Nature et technologies (FRQNT)
- Created
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2021-04-08Created from EPrint's datestamp field
- Updated
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2021-04-08Created from EPrint's last_modified field