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