arXiv subjects

Alan T. K. Wan

Publications and source records attributed to Alan T. K. Wan.

3 recordsLinked to original sources

arXiv2024

Bootstrap Model Averaging

Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method, known for its favorable properties, presents a new solution. In this paper, we propose a bootstrap model averaging approach that selects the weights by minimizing a bootstrap criterion. Our weight selection criterion can also be interpreted as a bootstrap aggregating. We demonstrate that the resultant estimator is asymptotically optimal in the sense that it achieves the lowest possible squared error loss. Furthermore, we establish the convergence rate of bootstrap weights tending to the theoretically optimal weights. Additionally, we derive the limiting distribution for our proposed model averaging estimator. Through simulation studies and empirical applications, we show that our proposed method often has better performance than other commonly used model selection and model averaging methods, and bootstrap variants.

stat.ME↗

arXiv2022

Model Averaging for Support Vector Machine by Cross-Validation

Support vector machine (SVM) is a well-known statistical technique for classification problems in machine learning and other fields. An important question for SVM is the selection of covariates (or features) for the model. Many studies have considered model selection methods. As is well-known, selecting one winning model over others can entail considerable instability in predictive performance due to model selection uncertainties. This paper advocates model averaging as an alternative approach, where estimates obtained from different models are combined in a weighted average. We propose a model weighting scheme and provide the theoretical underpinning for the proposed method. In particular, we prove that our proposed method yields a model average estimator that achieves the smallest hinge risk among all feasible combinations asymptotically. To remedy the computational burden due to a large number of feasible models, we propose a screening step to eliminate the uninformative features before combining the models. Results from real data applications and a simulation study show that the proposed method generally yields more accurate estimates than existing methods.

stat.ME↗

arXiv2019

On the asymptotic distribution of model averaging based on information criterion

Smoothed AIC (S-AIC) and Smoothed BIC (S-BIC) are very widely used in model averaging and are very easily to implement. Especially, the optimal model averaging method MMA and JMA have only been well developed in linear models. Only by modifying, they can be applied to other models. But S-AIC and S-BIC can be used in all situations where AIC and BIC can be calculated. In this paper, we study the asymptotic behavior of two commonly used model averaging estimators, the S-AIC and S-BIC estimators, under the standard asymptotic with general fixed parameter setup. In addition, the resulting coverage probability in Buckland et al. (1997) is not studied accurately, but it is claimed that it will be close to the intended. Our derivation make it possible to study accurately. Besides, we also prove that the confidence interval construction method in Hjort and Claeskens (2003) still works in linear regression with normal distribution error. Both the simulation and applied example support our theory conclusion.

stat.ME↗