Nonignorable missing data are frequently encountered in various settings, such as economics,sociology and biomedicine. We review statistical inference for nonignorable missing-data problems, including estimation, infl...Nonignorable missing data are frequently encountered in various settings, such as economics,sociology and biomedicine. We review statistical inference for nonignorable missing-data problems, including estimation, influence analysis and model selection. For estimation of meanfunctionals, we review semiparametric method and empirical likelihood (EL) approach. For estimation of parameters in exponential family nonlinear structural equation models, we introduceexpectation-maximisation algorithm, Bayesian approach, and Bayesian EL method. For influenceanalysis, we investigate the case-deletion method and local influence analysis method fromthe frequentist and Bayesian viewpoints. For model selection, we present the modified Akaikeinformation criterion and penalised method.展开更多
We thank five discussants for their thoughtful comments.All have made significant contributions to the general theme raised in our paper.We will try our best to answer each of points that five discussers have made.
We combine the robust criterion with the lasso penalty together for the high-dimensional threshold model.It estimates regression coefficients as well as the threshold parameter robustly that can be resistant to outlie...We combine the robust criterion with the lasso penalty together for the high-dimensional threshold model.It estimates regression coefficients as well as the threshold parameter robustly that can be resistant to outliers or heavy-tailed noises and perform variable selection simultaneously.We illustrate our approach with the absolute loss,the Huber’s loss,and the Tukey’s loss,it can also be extended to any other robust losses.Simulation studies are conducted to demonstrate the usefulness of our robust approach.Finally,we use our estimators to investigate the presence of a shift in the effect of debt on future GDP growth.展开更多
This paper proposes a new customer lifetime model:the Gamma/Weibull distribution(G/W).Similar to the Pareto/NBD model,we propose a G/W/NBD model by combining the G/W distribution with a negative binomial distribution(...This paper proposes a new customer lifetime model:the Gamma/Weibull distribution(G/W).Similar to the Pareto/NBD model,we propose a G/W/NBD model by combining the G/W distribution with a negative binomial distribution(NBD)and study its properties such as(i)the probability that a customer to be alive at a time point;(ii)the expectation and variance of the number of transactions for a customer during a fixed time period;(iii)the conditional expectation and conditional variance of the number of future transactions for a customer during a fixed time period.Several simulation studies are conducted to investigate the forecasting accuracy and flexibility of the proposed model.A CDNOW data set is analyzed by the proposed model.展开更多
基金This work was supported by the grants from the National Natural Science Foundation of China(Grant No.:11671349)the Key Projects of the National Natural Science Foundation of China(Grant No.:11731101).
文摘Nonignorable missing data are frequently encountered in various settings, such as economics,sociology and biomedicine. We review statistical inference for nonignorable missing-data problems, including estimation, influence analysis and model selection. For estimation of meanfunctionals, we review semiparametric method and empirical likelihood (EL) approach. For estimation of parameters in exponential family nonlinear structural equation models, we introduceexpectation-maximisation algorithm, Bayesian approach, and Bayesian EL method. For influenceanalysis, we investigate the case-deletion method and local influence analysis method fromthe frequentist and Bayesian viewpoints. For model selection, we present the modified Akaikeinformation criterion and penalised method.
基金This work was supported by the grants from the Key Projects of the National Natural Science Foundation of China[grant number 11731101]the National Natural Science Foundation of China[grant number 11671349].
文摘We thank five discussants for their thoughtful comments.All have made significant contributions to the general theme raised in our paper.We will try our best to answer each of points that five discussers have made.
基金the National Natural Science Foundation of China(No.11671349)the grants from the Key Projects of the National Natural Science Foundation of China(No.11731101).
文摘We combine the robust criterion with the lasso penalty together for the high-dimensional threshold model.It estimates regression coefficients as well as the threshold parameter robustly that can be resistant to outliers or heavy-tailed noises and perform variable selection simultaneously.We illustrate our approach with the absolute loss,the Huber’s loss,and the Tukey’s loss,it can also be extended to any other robust losses.Simulation studies are conducted to demonstrate the usefulness of our robust approach.Finally,we use our estimators to investigate the presence of a shift in the effect of debt on future GDP growth.
文摘This paper proposes a new customer lifetime model:the Gamma/Weibull distribution(G/W).Similar to the Pareto/NBD model,we propose a G/W/NBD model by combining the G/W distribution with a negative binomial distribution(NBD)and study its properties such as(i)the probability that a customer to be alive at a time point;(ii)the expectation and variance of the number of transactions for a customer during a fixed time period;(iii)the conditional expectation and conditional variance of the number of future transactions for a customer during a fixed time period.Several simulation studies are conducted to investigate the forecasting accuracy and flexibility of the proposed model.A CDNOW data set is analyzed by the proposed model.
