On consistency of wavelet estimator in nonparametric regression models

Xuejun Wang (), Yi Wu, Rui Wang and Shuhe Hu
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Xuejun Wang: Anhui University
Yi Wu: Anhui University
Rui Wang: Anhui University
Shuhe Hu: Anhui University

Statistical Papers, 2021, vol. 62, issue 2, No 16, 935-962

Abstract: Abstract In this paper, we mainly investigate the nonparametric regression model with repeated measurements based on extended negatively dependent (END, in short) errors. Based on the Rosenthal type inequality and the Marcinkiewicz–Zygmund type strong law of large numbers, the mean consistency, weak consistency, strong consistency, complete consistency and strong convergence rate of the wavelet estimator are established under some mild conditions, which generalize the corresponding ones for negatively associated errors. Some numerical simulations are presented to verify the validity of the theoretical results.

Keywords: Nonparametric regression model; END random variables; Wavelet estimator; Consistency; Marcinkiewicz–Zygmund type strong law of large numbers; 62G20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-019-01117-8

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