Frequentist Model Averaging and Applications to Bernoulli Trials

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.

FREQUENTIST MODEL AVERAGING ESTIMATION:A REVIEW

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.

Least Squares Model Averaging Based on Generalized Cross Validation

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.

Quantile Regression under Local Misspecification

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.