Applications of Mathematics

Applications of Mathematics, Vol. 68, No. 5, pp. 685-708, 2023

Density deconvolution with associated stationary data

Le Thi Hong Thuy, Cao Xuan Phuong

Received June 12, 2022. Published online September 3, 2023.

Abstract: We study the density deconvolution problem when the random variables of interest are an associated strictly stationary sequence and the random noises are i.i.d. with a nonstandard density. Based on a nonparametric strategy, we introduce an estimator depending on two parameters. This estimator is shown to be consistent with respect to the mean integrated squared error. Under additional regularity assumptions on the target function as well as on the density of noises, some error estimates are derived. Several numerical simulations are also conducted to illustrate the efficiency of our method.

Keywords: associated process; density deconvolution; nonstandard noise density

Classification MSC: 62G05, 62G07, 62G20

DOI: 10.21136/AM.2023.0135-22

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Le Thi Hong Thuy, Faculty of Fundamental Sciences, Van Lang University, 69/68 Dang Thuy Tram Street, Ward 13, Binh Thanh District, Ho Chi Minh City, Vietnam, e-mail: thuy.lth@vlu.edu.vn; Cao Xuan Phuong (corresponding author), Faculty of Mathematics and Statistics, Ton Duc Thang University, 19 Nguyen Huu Tho Street, Tan Phong Ward, District 7, Ho Chi Minh City, Vietnam, e-mail: caoxuanphuong@tdtu.edu.vn

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