The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation

Pötscher, Benedikt M. (2006): The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation. Published in: IMS Lecture Notes , Vol. 52, (2006): pp. 113-129.

Abstract

The finite-sample as well as the asymptotic distribution of Leung and Barron's (2006) model averaging estimator are derived in the context of a linear regression model. An impossibility result regarding the estimation of the finite-sample distribution of the model averaging estimator is obtained.

• Item Type: MPRA Paper
• Language: English
• Keywords: Model mixing; model aggregation; combination of estimators; model selection; finite sample distribution; asymptotic distribution; estimation of distribution
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C20 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C12 - Hypothesis Testing; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C13 - Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation and Selection

References

Billingsley, P. & F. Topsoe (1967): Uniformity in weak convergence. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 7, 1-16. Chandra, T.K. (1989): Multidimensional Polya's theorem. Bulletin of the Calcutta Mathematical Society 81, 227-231. Hoeting, J. A., Madigan, D. , Raftery, A. E. & C. T. Volinsky (1999): Bayesian model averaging: a tutorial [with discussion]. Statistical Science 19, 382--417. Hjort, N. L. & G. Claeskens (2003): Frequentist model average estimators. Journal of the American Statistical Association 98, 879--899. Leeb, H. (2005): The distribution of a linear predictor after model selection: conditional finite-sample distributions and asymptotic approximations. Journal of Statistical Planning and Inference 134, 64--89. Leeb, H. (2006): The distribution of a linear predictor after model selection: unconditional finite-sample distributions and asymptotic approximations. IMS Lecture Notes-Monograph Series, Vol. 49, J. Rojo (ed.), 291-311. Leeb, H. & B. M. Pötscher (2003): The finite-sample distribution of post-model-selection estimators and uniform versus nonuniform approximations. Econometric Theory 19, 100--142. Leeb, H. & B. M. Pötscher (2005a): Model Selection and Inference: Facts and Fiction. Econometric Theory 21, 21--59. Leeb, H. & B. M. Pötscher (2005b): Can one estimate the conditional distribution of post-model-selection estimators? Working Paper, Department of Statistics, University of Vienna. Annals of Statistics 34, forthcoming. Leeb, H. & B. M. Pötscher (2005c): Can one estimate the unconditional distribution of post-model-selection estimators? Working Paper, Department of Statistics, University of Vienna. Leeb, H. & B. M. Pötscher (2006): Performance limits for estimators of the risk or distribution of shrinkage-type estimators, and some general lower risk bound results. Econometric Theory 22, 69--97. Leung, G. & A. R. Barron (2006): Information theory and mixing least-squares regressions. IEEE Transactions on Information Theory, forthcoming. Magnus, J. R. (2002), Estimation of the mean of a univariate normal distribution with known variance. The Econometrics Journal 5, 225-236. Pötscher, B. M. (1991): Effects of model selection on inference. Econometric Theory 7, 163--185. Pötscher, B. M. & A. J. Novak (1998): The distribution of estimators after model selection: large and small sample results. Journal of Statistical Computation and Simulation 60, 19--56. Sen, P. K. (1979): Asymptotic properties of maximum likelihood estimators based on conditional specification. Annals of Statistics 7, 1019--1033. Sen P. K. & A. K. M. E. Saleh (1987): On preliminary test and shrinkage M-estimation in linear models. Annals of Statistics 15, 1580--1592. Yang, Y. (2000): Combining different regression procedures for adaptive regression. Journal of Multivariate Analysis 74, 135--161. Yang, Y. (2003): Regression with multiple candidate models: selecting or mixing?. Statistica Sinica 13, 783--809. Yang, Y. (2004): Combining forecasting procedures: some theoretical results. Econometric Theory 20, 176--222.