Deconvolution of a Cumulative Distribution Function with Some Non-standard Noise Densities

  • Dang Duc Trong
  • Cao Xuan Phuong


Let X be a continuous random variable having an unknown cumulative distribution function F. We study the problem of estimating F based on i.i.d. observations of a continuous random variable Y from the model Y = X + Z. Here, Z is a random noise distributed with known density g and is independent of X. We focus on some cases of g in which its Fourier transform can vanish on a countable subset of ℝ. We propose an estimator \(\hat F\) for F and then investigate upper bounds on convergence rate of \(\hat F\) under the root mean squared error. Some numerical experiments are also provided.


Deconvolution Cumulative distribution function Non-standard noise densities 

Mathematics Subject Classification (2010)

62G05 62G20 



We would like to thank the reviewers for their kind and careful reading of the paper and for helpful comments and suggestions which led to this improved version.

Funding Information

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2016.26.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceUniversity of Science, Vietnam National University Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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