Empirical likelihood for varying coefficient partially nonlinear model with missing responses
In this paper, we consider the statistical inferences for varying coefficient partially nonlinear model with missing responses. Firstly, we employ the profile nonlinear least squares estimation based on the weighted imputation method to estimate the unknown parameter and the nonparametric function,...
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doaj-c342b6a2fdab4862962cffb27c257dee2021-05-07T02:28:29ZengAIMS PressAIMS Mathematics2473-69882021-05-01677125715210.3934/math.2021418Empirical likelihood for varying coefficient partially nonlinear model with missing responsesLiqi Xia0Xiuli Wang1Peixin Zhao2Yunquan Song31. School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China3. College of Science, China University of Petroleum, Qingdao 266580, ChinaIn this paper, we consider the statistical inferences for varying coefficient partially nonlinear model with missing responses. Firstly, we employ the profile nonlinear least squares estimation based on the weighted imputation method to estimate the unknown parameter and the nonparametric function, meanwhile the asymptotic normality of the resulting estimators is proved. Secondly, we consider empirical likelihood inferences based on the weighted imputation method for the unknown parameter and nonparametric function, and propose an empirical log-likelihood ratio function for the unknown parameter vector in the nonlinear function and a residual-adjusted empirical log-likelihood ratio function for the nonparametric component, meanwhile construct relevant confidence regions. Thirdly, the response mean estimation is also studied. In addition, simulation studies are conducted to examine the finite sample performance of our methods, and the empirical likelihood approach based on the weighted imputation method (IEL) is further applied to a real data example.https://www.aimspress.com/article/doi/10.3934/math.2021418?viewType=HTMLvarying coefficient partially nonlinear modelprofile nonlinear least squares estimationweighted imputationmissing responsesempirical likelihood inferencesconfidence region |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Liqi Xia Xiuli Wang Peixin Zhao Yunquan Song |
spellingShingle |
Liqi Xia Xiuli Wang Peixin Zhao Yunquan Song Empirical likelihood for varying coefficient partially nonlinear model with missing responses AIMS Mathematics varying coefficient partially nonlinear model profile nonlinear least squares estimation weighted imputation missing responses empirical likelihood inferences confidence region |
author_facet |
Liqi Xia Xiuli Wang Peixin Zhao Yunquan Song |
author_sort |
Liqi Xia |
title |
Empirical likelihood for varying coefficient partially nonlinear model with missing responses |
title_short |
Empirical likelihood for varying coefficient partially nonlinear model with missing responses |
title_full |
Empirical likelihood for varying coefficient partially nonlinear model with missing responses |
title_fullStr |
Empirical likelihood for varying coefficient partially nonlinear model with missing responses |
title_full_unstemmed |
Empirical likelihood for varying coefficient partially nonlinear model with missing responses |
title_sort |
empirical likelihood for varying coefficient partially nonlinear model with missing responses |
publisher |
AIMS Press |
series |
AIMS Mathematics |
issn |
2473-6988 |
publishDate |
2021-05-01 |
description |
In this paper, we consider the statistical inferences for varying coefficient partially nonlinear model with missing responses. Firstly, we employ the profile nonlinear least squares estimation based on the weighted imputation method to estimate the unknown parameter and the nonparametric function, meanwhile the asymptotic normality of the resulting estimators is proved. Secondly, we consider empirical likelihood inferences based on the weighted imputation method for the unknown parameter and nonparametric function, and propose an empirical log-likelihood ratio function for the unknown parameter vector in the nonlinear function and a residual-adjusted empirical log-likelihood ratio function for the nonparametric component, meanwhile construct relevant confidence regions. Thirdly, the response mean estimation is also studied. In addition, simulation studies are conducted to examine the finite sample performance of our methods, and the empirical likelihood approach based on the weighted imputation method (IEL) is further applied to a real data example. |
topic |
varying coefficient partially nonlinear model profile nonlinear least squares estimation weighted imputation missing responses empirical likelihood inferences confidence region |
url |
https://www.aimspress.com/article/doi/10.3934/math.2021418?viewType=HTML |
work_keys_str_mv |
AT liqixia empiricallikelihoodforvaryingcoefficientpartiallynonlinearmodelwithmissingresponses AT xiuliwang empiricallikelihoodforvaryingcoefficientpartiallynonlinearmodelwithmissingresponses AT peixinzhao empiricallikelihoodforvaryingcoefficientpartiallynonlinearmodelwithmissingresponses AT yunquansong empiricallikelihoodforvaryingcoefficientpartiallynonlinearmodelwithmissingresponses |
_version_ |
1714602562121891840 |