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异方差模型平均的稀疏化赋权
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Abstract:
本文针对具有异方差误差的线性回归模型，在一种可行的Mallows’Cp准则提出的异方差稳健Cp(HRCp)模型平均方法基础上，考虑HRCp模型平均权重的稀疏性，使用坐标下降算法对异方差模型平均进行稀疏化赋权。数值模拟表明，用坐标下降算法改进的HRCp模型平均方法在候选模型较少或者中等、样本量不大时，相对于其他的模型平均方法有较小的损失风险，能更好的拟合模型。
Based on the averaging method of heteroscedasticity robust Cp (HRCp) model proposed by a feasi-ble Mallows’ Cp criterion, this paper considers the sparsity of the average weight of the HRCp model, and uses the coordinate-wise descent algorithm to sparse the average weight of the heteroscedas-ticity model. Numerical simulation shows that the improved HRCp model averaging method with coordinate-wise descent algorithm has less loss risk compared with other model averaging methods when the candidate models are few or medium and the sample size is not large, and can fit the model better.
| [1] | Andrews, D.W.K. (1991) Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Economet-rica, 59, 817-858. https://doi.org/10.2307/2938229 |
| [2] | Hansen, B.E. and Racine, J.S. (2012) Jackknife Model Averaging. Journal of Econometrics, 167, 38-46.
https://doi.org/10.1016/j.jeconom.2011.06.019 |
| [3] | Liu, Q.F and Okui, R. (2013) Heteroscedasticity-Robust CP Model Averaging. The Econometrics Journal, 16, 463-472.
https://doi.org/10.1111/ectj.12009 |
| [4] | Liu, C.A. (2015) Distribution Theory of the Least Squares Averaging Esti-mator. Journal of Econometrics, 186, 142-159. https://doi.org/10.1016/j.jeconom.2014.07.002 |
| [5] | Ando, T. and Li, K.C. (2014) A Model-Averaging Approach for Highdimensional Regression. Journal of the American Statistical As-sociation, 109, 254-265. https://doi.org/10.1080/01621459.2013.838168 |
| [6] | Charkhi, A., Claeskens, G. and Hansen, B.E. (2016) Minimum Mean Squared Error Model Averaging in Likelihood Models. Statistica Sinica, 26, 809-840. https://doi.org/10.5705/ss.202014.0067 |
| [7] | Zhang, X.Y., Yu, D.L., Zou, G.H. and Liang, H. (2016) Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models. Journal of the American Statistical Association, 111, 1775- 1790. https://doi.org/10.1080/01621459.2015.1115762 |
| [8] | Zhu, R., Wan, T.K.A., Zhang, X.Y. and Zou, G.H. (2019) A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model. Journal of the American Statistical Association, 114, 882-892.
https://doi.org/10.1080/01621459.2018.1456936 |
| [9] | Zhao, S.W, Ma, Y.Y., Wan, A.T.K., Zhang, X.Y. and Wang, S.Y. (2020) Model Averaging in a Multiplicative Heteroscedastic Model. Econometric Reviews, 39, 1100-1124. https://doi.org/10.1080/07474938.2020.1770995 |
| [10] | Zhang, X. and Liu, C.A. (2023) Model Averaging Prediction by K-Fold Cross-Validation. Journal of Econometrics, 235, 280-301. https://doi.org/10.1016/j.jeconom.2022.04.007 |
| [11] | Zhang, X.Y. and Zou, G.H. (2011) Model Averaging Method and Its Application in Forecast. Statistical Research, 28, 98-103. |
