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Shrinkage averaging estimation

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  • Michael Schomaker

Abstract

We discuss the impact of tuning parameter selection uncertainty in the context of shrinkage estimation and propose a methodology to account for problems arising from this issue: Transferring established concepts from model averaging to shrinkage estimation yields the concept of shrinkage averaging estimation (SAE) which reflects the idea of using weighted combinations of shrinkage estimators with different tuning parameters to improve overall stability, predictive performance and standard errors of shrinkage estimators. Two distinct approaches for an appropriate weight choice, both of which are inspired by concepts from the recent literature of model averaging, are presented: The first approach relates to an optimal weight choice with regard to the predictive performance of the final weighted estimator and its implementation can be realized via quadratic programming. The second approach has a fairly different motivation and considers the construction of weights via a resampling experiment. Focusing on Ridge, Lasso and Random Lasso estimators, the properties of the proposed shrinkage averaging estimators resulting from these strategies are explored by means of Monte-Carlo studies and are compared to traditional approaches where the tuning parameter is simply selected via cross validation criteria. The results show that the proposed SAE methodology can improve an estimators’ overall performance and reveal and incorporate tuning parameter uncertainty. As an illustration, selected methods are applied to some recent data from a study on leadership behavior in life science companies. Copyright Springer-Verlag 2012

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  • Michael Schomaker, 2012. "Shrinkage averaging estimation," Statistical Papers, Springer, vol. 53(4), pages 1015-1034, November.
    • Handle: RePEc:spr:stpapr:v:53:y:2012:i:4:p:1015-1034
    DOI: 10.1007/s00362-011-0405-2
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    1. Yuan, Zheng & Yang, Yuhong, 2005. "Combining Linear Regression Models: When and How?," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1202-1214, December.
    2. Hee‐Seok Oh & Doug Nychka & Tim Brown & Paul Charbonneau, 2004. "Period analysis of variable stars by robust smoothing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(1), pages 15-30, January.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Yan, Jun, 2007. "Enjoy the Joy of Copulas: With a Package copula," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i04).
    5. Xinyu Zhang & Alan T. K. Wan & Sherry Z. Zhou, 2011. "Focused Information Criteria, Model Selection, and Model Averaging in a Tobit Model With a Nonzero Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 132-142, June.
    6. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    7. Buchholz, Anika & Hollander, Norbert & Sauerbrei, Willi, 2008. "On properties of predictors derived with a two-step bootstrap model averaging approach--A simulation study in the linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2778-2793, January.
    8. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    9. Hansen, Bruce E. & Racine, Jeffrey S., 2012. "Jackknife model averaging," Journal of Econometrics, Elsevier, vol. 167(1), pages 38-46.
    10. Liang, Hua & Zou, Guohua & Wan, Alan T. K. & Zhang, Xinyu, 2011. "Optimal Weight Choice for Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1053-1066.
    11. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    12. Schomaker, Michael & Wan, Alan T.K. & Heumann, Christian, 2010. "Frequentist Model Averaging with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3336-3347, December.
    13. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    14. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
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    Citations

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    Cited by:

    1. Hui Xiao & Yiguo Sun, 2020. "Forecasting the Returns of Cryptocurrency: A Model Averaging Approach," JRFM, MDPI, vol. 13(11), pages 1-15, November.
    2. Hui Xiao & Yiguo Sun, 2019. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study," JRFM, MDPI, vol. 12(3), pages 1-16, June.
    3. Michael Schomaker & Christian Heumann, 2020. "When and when not to use optimal model averaging," Statistical Papers, Springer, vol. 61(5), pages 2221-2240, October.
    4. Lichun Wang & Yuan You & Heng Lian, 2015. "Convergence and sparsity of Lasso and group Lasso in high-dimensional generalized linear models," Statistical Papers, Springer, vol. 56(3), pages 819-828, August.
    5. Shangwei Zhao & Jun Liao & Dalei Yu, 2020. "Model averaging estimator in ridge regression and its large sample properties," Statistical Papers, Springer, vol. 61(4), pages 1719-1739, August.
    6. Hai Wang & Xinjie Chen & Nancy Flournoy, 2016. "The focused information criterion for varying-coefficient partially linear measurement error models," Statistical Papers, Springer, vol. 57(1), pages 99-113, March.
    7. Schomaker, Michael & Heumann, Christian, 2014. "Model selection and model averaging after multiple imputation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 758-770.
    8. Xiaochao Xia, 2021. "Model averaging prediction for nonparametric varying-coefficient models with B-spline smoothing," Statistical Papers, Springer, vol. 62(6), pages 2885-2905, December.
    9. David J. Olive, 2018. "Applications of hyperellipsoidal prediction regions," Statistical Papers, Springer, vol. 59(3), pages 913-931, September.
    10. Lasanthi C. R. Pelawa Watagoda & David J. Olive, 2021. "Bootstrapping multiple linear regression after variable selection," Statistical Papers, Springer, vol. 62(2), pages 681-700, April.

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