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 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.
