Wavelet-L1-estimation for non parametric location-scale models under a general dependence framework

We propose wavelet-L1-estimation for non parametric location-scale models from multiple subjects. The advantage of the wavelet is to avoid the restrictive smoothness requirement for the location and scale functions of the traditional smoothing approaches, such as kernel and local polynomial methods....

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Published inCommunications in statistics. Theory and methods Vol. 52; no. 10; pp. 3361 - 3381
Main Authors Zhou, Xingcai, Shen, Hao, Ni, Beibei, Xu, Yingzhi
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Ltd 15.05.2023
Subjects
Asymptotic properties
Nonparametric statistics
Normality
Polynomials
Scale models
Smoothness
Statistical inference
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Summary:We propose wavelet-L1-estimation for non parametric location-scale models from multiple subjects. The advantage of the wavelet is to avoid the restrictive smoothness requirement for the location and scale functions of the traditional smoothing approaches, such as kernel and local polynomial methods. Under a general dependence framework, which allows for longitudinal data and some spatially correlated data, uniform consistency, uniform Bahadur representation, and asymptotic normality for the proposed estimators of the location and scale functions are established. These results can be used to make asymptotically valid statistical inference.
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ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2021.1972312