In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually ...In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.展开更多
In applications,the traditional estimation procedure generally begins with model selection.Once a specific model is selected,subsequent estimation is conducted under the selected model withoutconsideration of the unce...In applications,the traditional estimation procedure generally begins with model selection.Once a specific model is selected,subsequent estimation is conducted under the selected model withoutconsideration of the uncertainty from the selection process.This often leads to the underreportingof variability and too optimistic confidence sets.Model averaging estimation is an alternative to thisprocedure,which incorporates model uncertainty into the estimation process.In recent years,therehas been a rising interest in model averaging from the frequentist perspective,and some importantprogresses have been made.In this paper,the theory and methods on frequentist model averagingestimation are surveyed.Some future research topics are also discussed.展开更多
Counting data without zero category often occurs in many fields,such as social studies,clinical trials and economic phenomenon analyses.Researchers usually show interest in describing the characteristics of the observ...Counting data without zero category often occurs in many fields,such as social studies,clinical trials and economic phenomenon analyses.Researchers usually show interest in describing the characteristics of the observed counts and the Poisson distribution is often preferred to model the counted data.Nevertheless,making marginal inference on the population mean is a challenging job when missing zero class occurs and the Poisson mean is considered as an alternative.In this paper,based on a so-called marginalized zero-truncated Poisson(ZTP)regression model,a novel SR-based EMFS algorithm is proposed to facilitate parameter estimation.To improve the prediction accuracy,this paper proposes a zero-truncated Poisson model averaging prediction that selects the optimal weight combination by minimizing a Kullback-Leibler(KL)divergence criterion.It is shown that the weight criterion is approximately unbiased about the expected KL loss.We further prove that the proposed prediction is asymptotically optimal in the sense that the KL-type loss and prediction risk are asymptotically identical to those of the infeasible best possible averaged prediction.Simulations and two empirical data applications are conducted to illustrate the proposed method.展开更多
Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new...Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.展开更多
The frequentist model averaging(FMA)and the focus information criterion(FIC)under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claes kens...The frequentist model averaging(FMA)and the focus information criterion(FIC)under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claes kens in 2003.One inconvenience,however,of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application to the case of quantile regression(QR).This as well as some other intrinsic merits of QR motivate us to study the FIC and FMA in a locally misspecified linear QR model.Specifically,we derive in this paper the explicit asymptotic risk expression for a general submodel-based QR estimator of a focus parameter.Then based on this asymptotic result,we develop the FIC and FMA in the current setting.Our theoretical development depends crucially on the convexity of the objective function,which makes possible to establish the asymptotics based on the existing convex stochastic process theory.Simulation studies are presented to illustrate the finite sample performance of the proposed method.The low birth weight data set is analyzed.展开更多
文摘In several instances of statistical practice, it is not uncommon to use the same data for both model selection and inference, without taking account of the variability induced by model selection step. This is usually referred to as post-model selection inference. The shortcomings of such practice are widely recognized, finding a general solution is extremely challenging. We propose a model averaging alternative consisting on taking into account model selection probability and the like-lihood in assigning the weights. The approach is applied to Bernoulli trials and outperforms Akaike weights model averaging and post-model selection estimators.
基金supported by the National Natural Science Foundation of China under Grant Nos.70625004,10721101,and 70221001
文摘In applications,the traditional estimation procedure generally begins with model selection.Once a specific model is selected,subsequent estimation is conducted under the selected model withoutconsideration of the uncertainty from the selection process.This often leads to the underreportingof variability and too optimistic confidence sets.Model averaging estimation is an alternative to thisprocedure,which incorporates model uncertainty into the estimation process.In recent years,therehas been a rising interest in model averaging from the frequentist perspective,and some importantprogresses have been made.In this paper,the theory and methods on frequentist model averagingestimation are surveyed.Some future research topics are also discussed.
基金the Editor-in-chief,an AE and two referees for their helpful comments and suggestions,which result in a significant improvement of the manuscriptthe National Natural Science Foundation of China(Grant No.12171483)+3 种基金the Fundamental Research Funds for the Central Universities(2722022BY020)National Natural Science Foundation of China(Grant Nos.71925007,72091212,12288201)the CAS Project for Young Scientists in Basic Research(Grant No.YSBR-008)a joint grant from Academy for Multidisciplinary Studies,Capital Normal University.
文摘Counting data without zero category often occurs in many fields,such as social studies,clinical trials and economic phenomenon analyses.Researchers usually show interest in describing the characteristics of the observed counts and the Poisson distribution is often preferred to model the counted data.Nevertheless,making marginal inference on the population mean is a challenging job when missing zero class occurs and the Poisson mean is considered as an alternative.In this paper,based on a so-called marginalized zero-truncated Poisson(ZTP)regression model,a novel SR-based EMFS algorithm is proposed to facilitate parameter estimation.To improve the prediction accuracy,this paper proposes a zero-truncated Poisson model averaging prediction that selects the optimal weight combination by minimizing a Kullback-Leibler(KL)divergence criterion.It is shown that the weight criterion is approximately unbiased about the expected KL loss.We further prove that the proposed prediction is asymptotically optimal in the sense that the KL-type loss and prediction risk are asymptotically identical to those of the infeasible best possible averaged prediction.Simulations and two empirical data applications are conducted to illustrate the proposed method.
基金by National Key R&D Program of China(2020AAA0105200)the Ministry of Science and Technology of China(Grant no.2016YFB0502301)+1 种基金the National Natural Science Foundation of China(Grant nos.11871294,12031016,11971323,71925007,72042019,72091212 and 12001559)a joint grant from the Academy for Multidisciplinary Studies,Capital Normal University.
文摘Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.
基金This paper is supported by the National Natural Science Foundation of China(No.11771049).
文摘The frequentist model averaging(FMA)and the focus information criterion(FIC)under a local framework have been extensively studied in the likelihood and regression setting since the seminal work of Hjort and Claes kens in 2003.One inconvenience,however,of the existing works is that they usually require the involved criterion function to be twice differentiable which thus prevents a direct application to the case of quantile regression(QR).This as well as some other intrinsic merits of QR motivate us to study the FIC and FMA in a locally misspecified linear QR model.Specifically,we derive in this paper the explicit asymptotic risk expression for a general submodel-based QR estimator of a focus parameter.Then based on this asymptotic result,we develop the FIC and FMA in the current setting.Our theoretical development depends crucially on the convexity of the objective function,which makes possible to establish the asymptotics based on the existing convex stochastic process theory.Simulation studies are presented to illustrate the finite sample performance of the proposed method.The low birth weight data set is analyzed.
