Within the sufficient dimension reduction framework,research on nonignorable missing data remains relatively scarce,primarily due to the associated identifiability issues.This paper considers the problem of sufficient...Within the sufficient dimension reduction framework,research on nonignorable missing data remains relatively scarce,primarily due to the associated identifiability issues.This paper considers the problem of sufficient dimension reduction when the response is subject to nonignorable missingness.By adopting a flexible semiparametric missingness mechanism to ensure identifiability,the authors construct three classes of estimating equations based on inverse probability weighting,regression imputation and augmented inverse probability weighting.The novel aspects of the proposed methods also include the incorporation of sufficient dimension reduction techniques in the implementation of these estimating equations to mitigate the high-dimensional effect,and the construction of the estimator for the conditional expectation of the estimating functions given both the covariates and the missingness indicator.The authors prove that the resulting three estimators are asymptotically normally distributed.Comprehensive simulation studies are conducted to assess the finite-sample performance of the proposed methods,and an application to PM2.5 concentration data is also presented.展开更多
Weconsider a model identification problem in which an outcome variable contains nonignorable missing values.Statistical inference requires a guarantee of the model identifiability to obtain estimators enjoying theoret...Weconsider a model identification problem in which an outcome variable contains nonignorable missing values.Statistical inference requires a guarantee of the model identifiability to obtain estimators enjoying theoretically reasonable properties such as consistency and asymptotic normality.Recently,instrumental or shadow variables,combined with the completeness condition in the outcome model,have been highlighted to make a model identifiable.In this paper,we elucidate the relationship between the completeness condition and model identifiability when the instrumental variable is categorical.We first show that when both the outcome and instrumental variables are categorical,the two conditions are equivalent.However,when one of the outcome and instrumental variables is continuous,the completeness condition may not necessarily hold,even for simple models.Consequently,we provide a sufficient condition that guarantees the identifiability of models exhibiting a monotone-likelihood property,a condition particularly useful in instances where establishing the completeness condition poses significant challenges.Using observed data,we demonstrate that the proposed conditions are easy to check for many practical models and outline their usefulness in numerical experiments and real data analysis.展开更多
In this paper,we consider parameter estimation,kink points testing and statistical inference for a longitudinal multi-kink expectile regression model with nonignorable dropout.In order to accommodate both within-subje...In this paper,we consider parameter estimation,kink points testing and statistical inference for a longitudinal multi-kink expectile regression model with nonignorable dropout.In order to accommodate both within-subject correlations and nonignorable dropout,the bias-corrected generalized estimating equations are constructed by combining the inverse probability weighting and quadratic inference function approaches.The estimators for the kink locations and regression coefficients are obtained by using the generalized method of moments.A selection procedure based on a modified BIC is applied to estimate the number of kink points.We theoreti-cally demonstrate the number selection consistency of kink points and the asymptotic normality of all estimators.A weighted cumulative sum type statistic is proposed to test the existence of kink effects at a given expectile,and its limiting distributions are derived under both the null and the local alternative hypotheses.Simulation studies show that the proposed estimators and test have desirable finite sample performance in both homoscedastic and heteroscedastic errors.An application to the Nation Growth,Lung and Health Study dataset is also presented.展开更多
基金supported by the Youth Program of the National Natural Science Foundation of China under Grant No.12401368the Youth Talent Special Support Program of Yunnan Provincial Xingdian Talent Support Plan+4 种基金the Scientific Research Fund Project of Yunnan Provincial Department of Education under Grant No.2020J0373the Scientific Research Fund Project of Yunnan University of Finance and Economics under Grant No.2022D11supported by the General Programs of the National Natural Science Foundation of China under Grant Nos.12271510 and 11871460the Innovative Research Group Program under Grant No.61621003a grant from the Key Laboratory of Random Complex Structures and Data Science,Chinese Academy of Sciences。
文摘Within the sufficient dimension reduction framework,research on nonignorable missing data remains relatively scarce,primarily due to the associated identifiability issues.This paper considers the problem of sufficient dimension reduction when the response is subject to nonignorable missingness.By adopting a flexible semiparametric missingness mechanism to ensure identifiability,the authors construct three classes of estimating equations based on inverse probability weighting,regression imputation and augmented inverse probability weighting.The novel aspects of the proposed methods also include the incorporation of sufficient dimension reduction techniques in the implementation of these estimating equations to mitigate the high-dimensional effect,and the construction of the estimator for the conditional expectation of the estimating functions given both the covariates and the missingness indicator.The authors prove that the resulting three estimators are asymptotically normally distributed.Comprehensive simulation studies are conducted to assess the finite-sample performance of the proposed methods,and an application to PM2.5 concentration data is also presented.
基金supported by MEXT Project for Seismology toward Research Innovation with Data of Earthquake(STAR-E)[Grant Number JPJ010217].
文摘Weconsider a model identification problem in which an outcome variable contains nonignorable missing values.Statistical inference requires a guarantee of the model identifiability to obtain estimators enjoying theoretically reasonable properties such as consistency and asymptotic normality.Recently,instrumental or shadow variables,combined with the completeness condition in the outcome model,have been highlighted to make a model identifiable.In this paper,we elucidate the relationship between the completeness condition and model identifiability when the instrumental variable is categorical.We first show that when both the outcome and instrumental variables are categorical,the two conditions are equivalent.However,when one of the outcome and instrumental variables is continuous,the completeness condition may not necessarily hold,even for simple models.Consequently,we provide a sufficient condition that guarantees the identifiability of models exhibiting a monotone-likelihood property,a condition particularly useful in instances where establishing the completeness condition poses significant challenges.Using observed data,we demonstrate that the proposed conditions are easy to check for many practical models and outline their usefulness in numerical experiments and real data analysis.
基金supported by the Fundamental Research Funds for the Central Universities and the National Natural Science Foundation of China[Grant Numbers 12271272 and 12001295].
文摘In this paper,we consider parameter estimation,kink points testing and statistical inference for a longitudinal multi-kink expectile regression model with nonignorable dropout.In order to accommodate both within-subject correlations and nonignorable dropout,the bias-corrected generalized estimating equations are constructed by combining the inverse probability weighting and quadratic inference function approaches.The estimators for the kink locations and regression coefficients are obtained by using the generalized method of moments.A selection procedure based on a modified BIC is applied to estimate the number of kink points.We theoreti-cally demonstrate the number selection consistency of kink points and the asymptotic normality of all estimators.A weighted cumulative sum type statistic is proposed to test the existence of kink effects at a given expectile,and its limiting distributions are derived under both the null and the local alternative hypotheses.Simulation studies show that the proposed estimators and test have desirable finite sample performance in both homoscedastic and heteroscedastic errors.An application to the Nation Growth,Lung and Health Study dataset is also presented.
