This paper considers the estimation problem of distribution functions and quantiles with nonignorable missing response data. Three approaches are developed to estimate distribution functions and quantiles, i.e., the H...This paper considers the estimation problem of distribution functions and quantiles with nonignorable missing response data. Three approaches are developed to estimate distribution functions and quantiles, i.e., the Horvtiz-Thompson-type method, regression imputation method and augmented inverse probability weighted approach. The propensity score is specified by a semiparametric expo- nential tilting model. To estimate the tilting parameter in the propensity score, the authors propose an adjusted empirical likelihood method to deal with the over-identified system. Under some regular conditions, the authors investigate the asymptotic properties of the proposed three estimators for distri- bution functions and quantiles, and find that these estimators have the same asymptotic variance. The jackknife method is employed to consistently estimate the asymptotic variances. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies.展开更多
In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of seconda...In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly due to correlated responses. Marginal models, such as generalized estimating equations (GEEs), have received much attention based on the assumption of the first two moments of the data and a working correlation structure. The confidence regions and hypothesis tests are constructed based on the asymptotic normality. This approach is sensitive to the misspecification of the variance function and the working correlation structure which may yield inefficient and inconsistent estimates leading to wrong conclusions. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its <span style="font-family:Verdana;">characteristics and asymptotic properties. We also provide an algorithm base</span><span style="font-family:Verdana;">d on EL principles for the estimation of the regression parameters and the construction of its confidence region. We have applied the proposed method in two case examples.</span>展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11671349 and 11601195the Scientific Research Innovation Team of Yunnan Province under Grant No.2015HC028the Natural Science Foundation of Jiangsu Province of China under Grant No.BK20160289
文摘This paper considers the estimation problem of distribution functions and quantiles with nonignorable missing response data. Three approaches are developed to estimate distribution functions and quantiles, i.e., the Horvtiz-Thompson-type method, regression imputation method and augmented inverse probability weighted approach. The propensity score is specified by a semiparametric expo- nential tilting model. To estimate the tilting parameter in the propensity score, the authors propose an adjusted empirical likelihood method to deal with the over-identified system. Under some regular conditions, the authors investigate the asymptotic properties of the proposed three estimators for distri- bution functions and quantiles, and find that these estimators have the same asymptotic variance. The jackknife method is employed to consistently estimate the asymptotic variances. Simulation studies are conducted to investigate the finite sample performance of the proposed methodologies.
文摘In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly due to correlated responses. Marginal models, such as generalized estimating equations (GEEs), have received much attention based on the assumption of the first two moments of the data and a working correlation structure. The confidence regions and hypothesis tests are constructed based on the asymptotic normality. This approach is sensitive to the misspecification of the variance function and the working correlation structure which may yield inefficient and inconsistent estimates leading to wrong conclusions. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its <span style="font-family:Verdana;">characteristics and asymptotic properties. We also provide an algorithm base</span><span style="font-family:Verdana;">d on EL principles for the estimation of the regression parameters and the construction of its confidence region. We have applied the proposed method in two case examples.</span>
