Least Squares Model Averaging
Abstract
This paper considers the problem of selection of weights for averaging across least squares estimates obtained from a set of models. Existing model average methods are based on exponential Akaike information criterion (AIC) and Bayesian information criterion (BIC) weights. In distinction, this paper proposes selecting the weights by minimizing a Mallows criterion, the latter an estimate of the average squared error from the model average fit. We show that our new Mallows model average (MMA) estimator is asymptotically optimal in the sense of achieving the lowest possible squared error in a class of discrete model average estimators. In a simulation experiment we show that the MMA estimator compares favorably with those based on AIC and BIC weights. The proof of the main result is an application of the work of Li (1987).
Citing Literature
Number of times cited according to CrossRef: 304
- Felix Chan, Laurent Pauwels, Sylvia Soltyk, Frequentist Averaging, Macroeconomic Forecasting in the Era of Big Data, 10.1007/978-3-030-31150-6_11, (329-357), (2020).
- Yang Feng, Qingfeng Liu, Ryo Okui, On the sparsity of Mallows model averaging estimator, Economics Letters, 10.1016/j.econlet.2019.108916, 187, (108916), (2020).
- Xiuping Chen, Guanghui Cai, Yan Gao, Shangwei Zhao, Asymptotic Optimality of the Nonnegative Garrote Estimator Under Heteroscedastic Errors, Journal of Systems Science and Complexity, 10.1007/s11424-020-8270-5, 33, 2, (545-562), (2020).
- Qingfeng Liu, Qingsong Yao, Guoqing Zhao, Model averaging estimation for conditional volatility models with an application to stock market volatility forecast, Journal of Forecasting, 10.1002/for.2659, 39, 5, (841-863), (2020).
- Qi Zhang, Tingting Tong, Shunyao Wu, Hybrid link prediction via model averaging, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2020.124772, (124772), (2020).
- Nikolay Gospodinov, Esfandiar Maasoumi, Generalized aggregation of misspecified models: With an application to asset pricing, Journal of Econometrics, 10.1016/j.jeconom.2020.07.010, (2020).
- Hongwei Zhang, Qiang He, Ben Jacobsen, Fuwei Jiang, Forecasting stock returns with model uncertainty and parameter instability, Journal of Applied Econometrics, 10.1002/jae.2747, 35, 5, (629-644), (2020).
- Fang Fang, Zhou Yu, Model averaging assisted sufficient dimension reduction, Computational Statistics & Data Analysis, 10.1016/j.csda.2020.106993, (106993), (2020).
- Mark F. J. Steel, Model Averaging and Its Use in Economics, Journal of Economic Literature, 10.1257/jel.20191385, 58, 3, (644), (2020).
- Josef Bajzik, Tomas Havranek, Zuzana Irsova, Jiri Schwarz, Estimating the Armington elasticity: The importance of study design and publication Bias, Journal of International Economics, 10.1016/j.jinteco.2020.103383, (103383), (2020).
- Yuying Sun, Yongmiao Hong, Tae-Hwy Lee, Shouyang Wang, Xinyu Zhang, Time-varying model averaging, Journal of Econometrics, 10.1016/j.jeconom.2020.02.006, (2020).
- Fang Fang, Minhan Liu, Limit of the optimal weight in least squares model averaging with non-nested models, Economics Letters, 10.1016/j.econlet.2020.109586, 196, (109586), (2020).
- Yundong Tu, Siwei Wang, Jackknife model averaging for expectile regressions in increasing dimension, Economics Letters, 10.1016/j.econlet.2020.109607, (109607), (2020).
- Tianming Gao, Vasilii Erokhin, Capturing a Complexity of Nutritional, Environmental, and Economic Impacts on Selected Health Parameters in the Russian High North, Sustainability, 10.3390/su12052151, 12, 5, (2151), (2020).
- Jen-Che Liao, Wen-Jen Tsay, OPTIMAL MULTISTEP VAR FORECAST AVERAGING, Econometric Theory, 10.1017/S0266466619000434, (1-28), (2020).
- Rongjie Jiang, Liming Wang, Yang Bai, Optimal model averaging estimator for semi-functional partially linear models, Metrika, 10.1007/s00184-020-00772-4, (2020).
- Zhihao Zhao, Guohua Zou, Average Estimation of Semiparametric Models for High-Dimensional Longitudinal Data, Journal of Systems Science and Complexity, 10.1007/s11424-020-9343-1, (2020).
- Mohitosh Kejriwal, Xuewen Yu, Generalized Forecast Averaging in Autoregressions with a Near Unit Root, The Econometrics Journal, 10.1093/ectj/utaa006, (2020).
- Rafael B. Barbosa, Roberto Tatiwa Ferreira, Thibério Mota da Silva, Previsão de Variáveis Macroeconômicas Brasileiras usando Modelos de Séries Temporais de Alta Dimensão, Estudos Econômicos (São Paulo), 10.1590/0101-41615013rrt, 50, 1, (67-98), (2020).
- Shangwei Zhao, Yanyuan Ma, Alan T. K. Wan, Xinyu Zhang, Shouyang Wang, Model averaging in a multiplicative heteroscedastic model, Econometric Reviews, 10.1080/07474938.2020.1770995, (1-25), (2020).
- Antonio Pacifico, Robust open Bayesian analysis: Overfitting, model uncertainty, and endogeneity issues in multiple regression models, Econometric Reviews, 10.1080/07474938.2020.1770996, (1-29), (2020).
- Shu-Hui Yu, Chor-yiu (CY) Sin, On asymptotic risk of selecting models for possibly nonstationary time-series, Econometric Reviews, 10.1080/07474938.2020.1777709, (1-28), (2020).
- Xinyu Zhang, A NEW STUDY ON ASYMPTOTIC OPTIMALITY OF LEAST SQUARES MODEL AVERAGING, Econometric Theory, 10.1017/S0266466620000055, (1-20), (2020).
- Céline Cunen, Nils Lid Hjort, Confidence Distributions for FIC Scores, Econometrics, 10.3390/econometrics8030027, 8, 3, (27), (2020).
- Yuting Wei, Qihua Wang, Wei Liu, Model averaging for linear models with responses missing at random, Annals of the Institute of Statistical Mathematics, 10.1007/s10463-020-00759-y, (2020).
- Yin-Wong Cheung, Wenhao Wang, A Jackknife Model Averaging Analysis of RMB Misalignment Estimates, Journal of International Commerce, Economics and Policy, 10.1142/S1793993320500076, (2050007), (2020).
- Anders Isaksson, Chenjun Shang, Robin C. Sickles, Nonstructural analysis of productivity growth for the industrialized countries: a jackknife model averaging approach, Econometric Reviews, 10.1080/07474938.2020.1788820, (1-38), (2020).
- Christian Mandl, Stefan Minner, Data-Driven Optimization for Commodity Procurement Under Price Uncertainty, Manufacturing & Service Operations Management, 10.1287/msom.2020.0890, (2020).
- Jialiang Li, Jing Lv, Alan T. K. Wan, Jun Liao, AdaBoost Semiparametric Model Averaging Prediction for Multiple Categories, Journal of the American Statistical Association, 10.1080/01621459.2020.1790375, (1-15), (2020).
- Stefano Battista, Massimo Conti, Simone Orcioni, Methodology for Modeling and Comparing Video Codecs: HEVC, EVC, and VVC, Electronics, 10.3390/electronics9101579, 9, 10, (1579), (2020).
- Barry L. Nelson, Alan T. K. Wan, Guohua Zou, Xinyu Zhang, Xi Jiang, Reducing Simulation Input-Model Risk via Input Model Averaging, INFORMS Journal on Computing, 10.1287/ijoc.2020.0994, (2020).
- Haili Zhang, Guohua Zou, Cross-Validation Model Averaging for Generalized Functional Linear Model, Econometrics, 10.3390/econometrics8010007, 8, 1, (7), (2020).
- Michael Declan Power, Yuexiao Dong, Comment on ‘Review of sparse sufficient dimension reduction’, Statistical Theory and Related Fields, 10.1080/24754269.2020.1829394, (1-2), (2020).
- JIANCHUN FANG, WANSHAN WU, ZHOU LU, EUNHO CHO, USING BAIDU INDEX TO NOWCAST MOBILE PHONE SALES IN CHINA, The Singapore Economic Review, 10.1142/S021759081743007X, 64, 01, (83-96), (2019).
- Timothy Cogley, Richard Startz, Robust Estimation of ARMA Models with Near Root Cancellation, Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A, 10.1108/S0731-90532019000040A007, (133-155), (2019).
- Jun Liao, Guohua Zou, Corrected Mallows criterion for model averaging, Computational Statistics & Data Analysis, 10.1016/j.csda.2019.106902, (106902), (2019).
- Bai Huang, Tae-Hwy Lee, Aman Ullah, Stein-like Shrinkage Estimation of Panel Data Models with Common Correlated Effects, Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A, 10.1108/S0731-90532019000040A011, (249-274), (2019).
- Xu Cheng, Zhipeng Liao, Ruoyao Shi, On uniform asymptotic risk of averaging GMM estimators, Quantitative Economics, 10.3982/QE711, 10, 3, (931-979), (2019).
- Wen-Jen Tsay, Estimating Cartel Damages with Model Averaging Approaches, SSRN Electronic Journal, 10.2139/ssrn.3403955, (2019).
- Sameer Mathur, Ashish Dubey, Determinants of Hotel Room Prices in India, Advances in Hospitality and Leisure, 10.1108/S1745-354220190000015010, (161-171), (2019).
- Neil R. Ericsson, Andrew B. Martinez, Evaluating Government Budget Forecasts, The Palgrave Handbook of Government Budget Forecasting, 10.1007/978-3-030-18195-6_3, (37-69), (2019).
- Jun Liao, Guohua Zou, Yan Gao, Spatial Mallows model averaging for geostatistical models, Canadian Journal of Statistics, 10.1002/cjs.11497, 47, 3, (336-351), (2019).
- Wendun Wang, Xinyu Zhang, Richard Paap, To pool or not to pool: What is a good strategy for parameter estimation and forecasting in panel regressions?, Journal of Applied Econometrics, 10.1002/jae.2696, 34, 5, (724-745), (2019).
- Xinyu Zhang, Yanyuan Ma, Raymond J. Carroll, MALMEM: model averaging in linear measurement error models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 10.1111/rssb.12317, 81, 4, (763-779), (2019).
- Christopher F. Parmeter, Alan T. K. Wan, Xinyu Zhang, Model averaging estimators for the stochastic frontier model, Journal of Productivity Analysis, 10.1007/s11123-019-00547-8, 51, 2-3, (91-103), (2019).
- K Alhorn, K Schorning, H Dette, Optimal designs for frequentist model averaging, Biometrika, 10.1093/biomet/asz036, (2019).
- Qingfeng Liu, Andrey L. Vasnev, A Combination Method for Averaging OLS and GLS Estimators, Econometrics, 10.3390/econometrics7030038, 7, 3, (38), (2019).
- Priyam Mitra, Heng Lian, Ritwik Mitra, Hua Liang, Min-ge Xie, A general framework for frequentist model averaging, Science China Mathematics, 10.1007/s11425-018-9403-x, (2019).
- Yue Qiu, Yu Ren, Tian Xie, Weighing asset pricing factors: a least squares model averaging approach, Quantitative Finance, 10.1080/14697688.2019.1602276, (1-15), (2019).
- Hui Xiao, Yiguo Sun, On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study, Journal of Risk and Financial Management, 10.3390/jrfm12030109, 12, 3, (109), (2019).
- Baihua He, Fangli Dong, Model averaging with privacy-preserving, Communications in Statistics - Simulation and Computation, 10.1080/03610918.2019.1670842, (1-14), (2019).
- Tian Xie, Forecast Bitcoin Volatility with Least Squares Model Averaging, Econometrics, 10.3390/econometrics7030040, 7, 3, (40), (2019).
- Guozhi Hu, Weihu Cheng, Jie Zeng, Model averaging by jackknife criterion for varying-coefficient partially linear models, Communications in Statistics - Theory and Methods, 10.1080/03610926.2019.1580736, (1-19), (2019).
- Xinyu Zhang, Guohua Zou, Hua Liang, Raymond J. Carroll, Parsimonious Model Averaging With a Diverging Number of Parameters, Journal of the American Statistical Association, 10.1080/01621459.2019.1604363, (1-26), (2019).
- Shou-Yung Yin, Chu-An Liu, Chang-Ching Lin, Focused Information Criterion and Model Averaging for Large Panels With a Multifactor Error Structure, Journal of Business & Economic Statistics, 10.1080/07350015.2019.1623044, (1-30), (2019).
- Guannan Liu, Wei Long, Xinyu Zhang, Qi Li, DETECTING FINANCIAL DATA DEPENDENCE STRUCTURE BY AVERAGING MIXTURE COPULAS, Econometric Theory, 10.1017/S0266466618000270, 35, 4, (777-815), (2018).
- Chor-yiu Sin, Shu-Hui Yu, Order selection for possibly infinite-order non-stationary time series, AStA Advances in Statistical Analysis, 10.1007/s10182-018-00333-1, 103, 2, (187-216), (2018).
- Xinyu Zhang, Chu-An Liu, INFERENCE AFTER MODEL AVERAGING IN LINEAR REGRESSION MODELS, Econometric Theory, 10.1017/S0266466618000269, 35, 4, (816-841), (2018).
- Shaobo Jin, Sebastian Ankargren, Frequentist Model Averaging in Structural Equation Modelling, Psychometrika, 10.1007/s11336-018-9624-y, 84, 1, (84-104), (2018).
- Rong Zhu, Alan T. K. Wan, Xinyu Zhang, Guohua Zou, A Mallows-Type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model, Journal of the American Statistical Association, 10.1080/01621459.2018.1456936, 114, 526, (882-892), (2018).
- Jan Lohmeyer, Franz Palm, Hanno Reuvers, Jean-Pierre Urbain, Focused information criterion for locally misspecified vector autoregressive models, Econometric Reviews, 10.1080/07474938.2017.1409410, 38, 7, (763-792), (2018).
- Fang Fang, Wei Lan, Jingjing Tong, Jun Shao, Model Averaging for Prediction With Fragmentary Data, Journal of Business & Economic Statistics, 10.1080/07350015.2017.1383263, 37, 3, (517-527), (2018).
- Xinyu Zhang, Jihai Yu, Spatial weights matrix selection and model averaging for spatial autoregressive models, Journal of Econometrics, 10.1016/j.jeconom.2017.05.021, 203, 1, (1-18), (2018).
- O.B. Olesen, J. Ruggiero, An improved Afriat–Diewert–Parkan nonparametric production function estimator, European Journal of Operational Research, 10.1016/j.ejor.2017.07.057, 264, 3, (1172-1188), (2018).
- Jie Zeng, Weihu Cheng, Guozhi Hu, Yaohua Rong, Model averaging procedure for varying-coefficient partially linear models with missing responses, Journal of the Korean Statistical Society, 10.1016/j.jkss.2018.04.004, 47, 3, (379-394), (2018).
- TIAGO FREIRE, WAGE SUBSIDIES AND THE LABOR SUPPLY OF OLDER PEOPLE: EVIDENCE FROM SINGAPORE’S WORKFARE INCOME SUPPLEMENT SCHEME, The Singapore Economic Review, 10.1142/S0217590815500964, 63, 05, (1101-1139), (2018).
- Shangwei Zhao, Aman Ullah, Xinyu Zhang, A class of model averaging estimators, Economics Letters, 10.1016/j.econlet.2017.10.023, 162, (101-106), (2018).
- Alexander Vosseler, Enzo Weber, Forecasting seasonal time series data: a Bayesian model averaging approach, Computational Statistics, 10.1007/s00180-018-0801-3, 33, 4, (1733-1765), (2018).
- Bruce Hansen, Jeffrey Racine, Bootstrap Model Averaging Unit Root Inference, SSRN Electronic Journal, 10.2139/ssrn.3156028, (2018).
- Rodrigo A. González, Cristian R. Rojas, A fully Bayesian approach to kernel-based regularization for impulse response estimation, IFAC-PapersOnLine, 10.1016/j.ifacol.2018.09.123, 51, 15, (186-191), (2018).
- Qi Lin, Technical analysis and stock return predictability: An aligned approach, Journal of Financial Markets, 10.1016/j.finmar.2017.09.003, 38, (103-123), (2018).
- David Fletcher, David Fletcher, Frequentist Model Averaging, Model Averaging, 10.1007/978-3-662-58541-2_3, (57-97), (2018).
- Nikita A. Moiseev, Aleksander S. Sorokin, Interval forecast for model averaging methods, Model Assisted Statistics and Applications, 10.3233/MAS-180427, 13, 2, (161-172), (2018).
- Dongxue Zhang, Zhiming Xia, Weighted-averaging estimator for possible threshold in segmented linear regression model, Journal of Statistical Planning and Inference, 10.1016/j.jspi.2018.09.008, (2018).
- Jun Liao, Xianpeng Zong, Xinyu Zhang, Guohua Zou, Model averaging based on leave-subject-out cross-validation for vector autoregressions, Journal of Econometrics, 10.1016/j.jeconom.2018.10.007, (2018).
- Jeffrey Y. Jung, Jeffrey D. Niemann, Blair P. Greimann, Combining Predictions and Assessing Uncertainty from Sediment Transport Equations Using Multivariate Bayesian Model Averaging, Journal of Hydraulic Engineering, 10.1061/(ASCE)HY.1943-7900.0001436, 144, 4, (04018008), (2018).
- Qingfeng Liu, Qingsong Yao, Guoqing Zhao, Model Averaging Estimation for Conditional Volatility Models, SSRN Electronic Journal, 10.2139/ssrn.3282578, (2018).
- Jingli Wang, Jialiang Li, Semiparametric model averaging prediction: a Bayesian approach, Australian & New Zealand Journal of Statistics, 10.1111/anzs.12249, 60, 4, (407-422), (2018).
- Jialiang Li, Xiaochao Xia, Weng Kee Wong, David Nott, Varying‐coefficient semiparametric model averaging prediction, Biometrics, 10.1111/biom.12904, 74, 4, (1417-1426), (2018).
- Tomas Havranek, Zuzana Irsova, Olesia Zeynalova, Tuition Fees and University Enrolment: A Meta‐Regression Analysis, Oxford Bulletin of Economics and Statistics, 10.1111/obes.12240, 80, 6, (1145-1184), (2018).
- Julia Kapraun, Matthias Pelster, Relying on Others' Investment Skills: About the Dynamics of Relationships in Social Trading Networks, SSRN Electronic Journal, 10.2139/ssrn.2973194, (2018).
- Hannah E. Correia, Spatiotemporally explicit model averaging for forecasting of Alaskan groundfish catch, Ecology and Evolution, 10.1002/ece3.4488, 8, 24, (12308-12321), (2018).
- Biao Guo, Qian Han, Hai Lin, Are there gains from using information over the surface of implied volatilities?, Journal of Futures Markets, 10.1002/fut.21903, 38, 6, (645-672), (2018).
- Rengyi Xu, Devan V. Mehrotra, Pamela A. Shaw, Incorporating baseline measurements into the analysis of crossover trials with time‐to‐event endpoints, Statistics in Medicine, 10.1002/sim.7834, 37, 23, (3280-3292), (2018).
- Longmei Chen, Alan T. K. Wan, Geoffrey Tso, Xinyu Zhang, A model averaging approach for the ordered probit and nested logit models with applications, Journal of Applied Statistics, 10.1080/02664763.2018.1450367, 45, 16, (3012-3052), (2018).
- Jia Chen, Degui Li, Oliver Linton, Zudi Lu, Semiparametric Ultra-High Dimensional Model Averaging of Nonlinear Dynamic Time Series, Journal of the American Statistical Association, 10.1080/01621459.2017.1302339, 113, 522, (919-932), (2018).
- Chenglong Ye, Yi Yang, Yuhong Yang, Sparsity Oriented Importance Learning for High-Dimensional Linear Regression, Journal of the American Statistical Association, 10.1080/01621459.2017.1377080, 113, 524, (1797-1812), (2018).
- Yan Gao, Xinyu Zhang, Shouyang Wang, Terence Tai-leung Chong, Guohua Zou, Frequentist model averaging for threshold models, Annals of the Institute of Statistical Mathematics, 10.1007/s10463-017-0642-9, (2018).
- Xinyu Zhang, Yafei Zheng, Shouyang Wang, A Demand Forecasting Method Based on Stochastic Frontier Analysis and Model Average: An Application in Air Travel Demand Forecasting, Journal of Systems Science and Complexity, 10.1007/s11424-018-7093-0, (2018).
- John Galbraith, Douglas Hodgson, Econometric Fine Art Valuation by Combining Hedonic and Repeat-Sales Information, Econometrics, 10.3390/econometrics6030032, 6, 3, (32), (2018).
- Shangwei Zhao, Jun Liao, Dalei Yu, Model averaging estimator in ridge regression and its large sample properties, Statistical Papers, 10.1007/s00362-018-1002-4, (2018).
- Michael Schomaker, Christian Heumann, When and when not to use optimal model averaging, Statistical Papers, 10.1007/s00362-018-1048-3, (2018).
- Jie Zeng, Weihu Cheng, Guozhi Hu, Yaohua Rong, Model selection and model averaging for semiparametric partially linear models with missing data, Communications in Statistics - Theory and Methods, 10.1080/03610926.2017.1410717, 48, 2, (381-395), (2017).
- Tao Huang, Jialiang Li, Semiparametric model average prediction in panel data analysis, Journal of Nonparametric Statistics, 10.1080/10485252.2017.1404061, 30, 1, (125-144), (2017).
- Katja Heinisch, Rolf Scheufele, Bottom-up or direct? Forecasting German GDP in a data-rich environment, Empirical Economics, 10.1007/s00181-016-1218-x, 54, 2, (705-745), (2017).
- Matthias Pelster, Johannes Vilsmeier, The determinants of CDS spreads: evidence from the model space, Review of Derivatives Research, 10.1007/s11147-017-9134-6, 21, 1, (63-118), (2017).
- Rong Zhu, Guohua Zou, Xinyu Zhang, Model averaging for multivariate multiple regression models, Statistics, 10.1080/02331888.2017.1367794, 52, 1, (205-227), (2017).
- Sebastian Ankargren, Shaobo Jin, On the least-squares model averaging interval estimator, Communications in Statistics - Theory and Methods, 10.1080/03610926.2017.1300272, 47, 1, (118-132), (2017).
- Esteban Fernández-Vázquez, Blanca Moreno, Entropy Econometrics for combining regional economic forecasts: A Data-Weighted Prior Estimator, Journal of Geographical Systems, 10.1007/s10109-017-0259-9, 19, 4, (349-370), (2017).
- Jun Liao, Guohua Zou, Yan Gao, Optimal model averaging by data perturbation for spatial noisy data, Environmental and Ecological Statistics, 10.1007/s10651-017-0377-z, 24, 3, (415-431), (2017).
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