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Jackknife Model Averaging for Composite Quantile Regression

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Abstract

In this paper, the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters. Different from the traditional model averaging for quantile regression which considers only a single quantile, the proposed model averaging estimator is based on multiple quantiles. The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights. The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error. Simulation studies are conducted to demonstrate the finite sample performance of the new model averaging estimator. The proposed method is also applied to the analysis of the stock returns data and the wage data.

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References

  1. Akaike H, Information theory and an extension of the maximum likelihood principle, Proceedings of International Symposium on Information Theory, 1973, 267–281.

  2. Schwarz G, Estimating the dimension of a model, Annals of Statistics, 1978, 6: 461–464.

    Article  MathSciNet  Google Scholar 

  3. Mallows C L, Some comments on Cp, Technometrics, 1973, 15: 661–675.

    Google Scholar 

  4. Tibshirani R, Regression shrinkage and selection via the LASSO: A retrospective, Journal of the Royal Statistical Society, Series B, 1996, 58: 267–288.

    Article  MathSciNet  Google Scholar 

  5. Fan J and Li R, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American Statistical Association, 2001, 96: 1348–1360.

    Article  MathSciNet  Google Scholar 

  6. Koenker R and Bassett G, Regression quantiles, Econometrica, 1978, 46: 33–50.

    Article  MathSciNet  Google Scholar 

  7. Koenker R and Hallock K, Quantile regression, Journal of Economic Perspectives, 2001, 15: 143–156.

    Article  Google Scholar 

  8. Koenker R and Geling O, Reappraising medfly longevity: A quantile regression survival analysis, Journal of the American Statistical Association, 2001, 96: 458–468.

    Article  MathSciNet  Google Scholar 

  9. Agarwal G and Sun Y, Bivariate functional quantile envelopes with application to radiosonde wind data, Technometrics, 2021, 63: 199–211.

    Article  MathSciNet  Google Scholar 

  10. Koenker R, Quantile Regression, Cambridge University Press, Cambridge, 2005.

    Book  Google Scholar 

  11. Yu K, Lu Z, and Stander J, Quantile regression: Applications and current research areas, Journal of the Royal Statistical Society, Series D, 2021, 52: 331–350.

    MathSciNet  Google Scholar 

  12. Machado J A, Robust model selection and M-estimation, Econometric Theory, 1993, 9: 478–493.

    Article  MathSciNet  Google Scholar 

  13. Koenker R, Quantile regression for longitudinal data, Journal of Multivariate Analysis, 2004, 91: 74–89.

    Article  MathSciNet  Google Scholar 

  14. Li Y and Zhu J, L1-norm quantile regression, Journal of Computational & Graphical Statistics, 2008, 17: 163–185.

    Article  MathSciNet  Google Scholar 

  15. Wu Y and Liu Y, Variable selection in quantile regression, Statistica Sinica, 2009, 19: 801–817.

    MathSciNet  Google Scholar 

  16. Alhamzawi R, Yu K, and Benoit D F, Bayesian adaptive LASSO quantile regression, Statistical Modelling, 2012, 12: 279–297.

    Article  MathSciNet  Google Scholar 

  17. Alkenani A and Yu K, Penalized single-index quantile regression, International Journal of Statistics & Probability, 2013, 2: 12–30.

    Article  Google Scholar 

  18. Li Q, Xi R, and Lin N, Bayesian regularized quantile regression, Bayesian Analysis, 2010, 5: 533–556.

    Article  MathSciNet  Google Scholar 

  19. Yuan Y and Yin G, Bayesian quantile regression for longitudinal studies with nonignorable missing data, Biometrics, 2010, 66: 105–114.

    Article  MathSciNet  Google Scholar 

  20. Zou H and Yuan M, Composite quantile regression and the oracle model selection theory, Annals of Statistics, 2008, 36: 1108–1126.

    Article  MathSciNet  Google Scholar 

  21. Zou H and Yuan M, Regularized simultaneous model selection in multiple quantiles regression, Computational Statistics and Data Analysis, 2008, 52: 5296–5304.

    Article  MathSciNet  Google Scholar 

  22. Jiang R, Zhou Z, Qian W, et al., Single-index composite quantile regression, Journal of the Korean Statistical Society, 2012, 41: 323–332.

    Article  MathSciNet  Google Scholar 

  23. Jiang X, Jiang J, and Song X, Oracle model selection for nonlinear models based on weighted composite quantile regression, Statistica Sinica, 2012, 22: 1479–1506.

    MathSciNet  Google Scholar 

  24. Kai B, Li R, and Zou H, Local composite quantile regression smoothing: An efficient and safe alternative to local polynomial regression, Journal of the Royal Statistical Society, Series B, 2010, 72: 49–69.

    Article  MathSciNet  Google Scholar 

  25. Zhao P, Zhou X, and Lin L, Empirical likelihood for composite quantile regression modeling, Journal of Applied Mathematics & Computing, 2015, 48: 321–333.

    Article  MathSciNet  Google Scholar 

  26. Claeskens G, Statistical model choice, Annual Review of Statistics and Its Application, 2016, 3: 233–256.

    Article  Google Scholar 

  27. Leeb H and Pötscher B M, Can one estimate the conditional distribution of post-model-selection estimators? Annals of Statistics, 2006, 34: 2254–2591.

    Article  MathSciNet  Google Scholar 

  28. Buckland S T, Burnham K P, and Augustin N H, Model selection: An integral part of inference, Biometrics, 1997, 53: 603–618.

    Article  Google Scholar 

  29. Hjort N L and Claeskens G, Focused information criteria and model averaging for the Cox hazard regression model, Journal of the American Statistical Association, 2006, 101: 1449–1464.

    Article  MathSciNet  Google Scholar 

  30. Zhang X and Liang H, Focused information criterion and model averaging for generalized additive partial linear models, Annals of Statistics, 2011, 39: 174–200.

    Article  MathSciNet  Google Scholar 

  31. Yang Y, Adaptive regression by mixing, Journal of the American Statistical Association, 2001, 96: 574–588.

    Article  MathSciNet  Google Scholar 

  32. Hansen B E, Least squares model averaging, Econometrica, 2007, 75: 1175–1189.

    Article  MathSciNet  Google Scholar 

  33. Hansen B E, Least squares forecast averaging, Journal of Econometrics, 2008, 146: 342–350.

    Article  MathSciNet  Google Scholar 

  34. Wan A T, Zhang X, and Zou G, Least squares model averaging by mallows criterion, Journal of Econometrics, 2010, 156: 277–283.

    Article  MathSciNet  Google Scholar 

  35. Liang H, Zou G, Wan A T, et al., Optimal weight choice for frequentist model average estimators, Journal of the American Statistical Association, 2011, 106: 1053–1066.

    Article  MathSciNet  Google Scholar 

  36. Wan A T, Zhang X, and Wang S, Frequentist model averaging for multinomial and ordered logit models, International Journal of Forecasting, 2014, 30: 118–128.

    Article  Google Scholar 

  37. Ando T and Li K C, A model-averaging approach for high-dimensional regression, Journal of American Statistical Association, 2014, 109: 254–265.

    Article  MathSciNet  Google Scholar 

  38. Hansen B E and Racine J S, Jackknife model averaging, Journal of Econometrics, 2012, 167: 38–46.

    Article  MathSciNet  Google Scholar 

  39. Zhang X, Wan A T, and Zou G, Model averaging by jackknife criterion in models with dependent data, Journal of Econometrics, 2013, 174: 82–94.

    Article  MathSciNet  Google Scholar 

  40. Gao Y, Zhang X, Wang S, et al., Model averaging based on leave-subject-out cross-validation, Journal of Econometrics, 2016, 192: 139–151.

    Article  MathSciNet  Google Scholar 

  41. Liao J, Zong X, Zhang X, et al., Model averaging based on leave-subject-out cross-validation for vector autoregressions, Journal of Econometrics, 2019, 209: 35–60.

    Article  MathSciNet  Google Scholar 

  42. Zhang X, Zou G, and Carroll R, Model averaging based on Kullback-Leibler distance, Statistica Sinica, 2015, 25: 1583–1598.

    MathSciNet  Google Scholar 

  43. Lu X and Su L, Jackknife model averaging for quantile regressions, Journal of Econometrics, 2015, 188: 40–58.

    Article  MathSciNet  Google Scholar 

  44. Shan K and Yang Y, Combining regression quantile estimators, Statistica Sinica, 2009, 19: 1171–1191.

    MathSciNet  Google Scholar 

  45. Wang M, Zhang X, Wan A T, et al., Jackknife model averaging for high-dimensional quantile regression, Biometrics, 2023, 79(1): 178–189.

    Article  MathSciNet  Google Scholar 

  46. Wang H, Inference on quantile regression for heteroscedastic mixed models, Statistica Sinica, 2009, 19: 1247–1261.

    MathSciNet  Google Scholar 

  47. Wang L, Wu Y, and Li R, Quantile regression for analyzing heterogeneity in ultra-high dimension, Journal of the American Statistical Association, 2012, 107: 214–222.

    Article  MathSciNet  Google Scholar 

  48. Fan J and Peng H, On nonconcave penalized likelihood with diverging number of parameters, Annals of Statistics, 2004, 32: 928–961.

    Article  MathSciNet  Google Scholar 

  49. Koenker R, Ng P, and Portnoy S, Quantile regression splines, Biometrika, 1994, 81: 673–680.

    Article  MathSciNet  Google Scholar 

  50. Jin S, Su L, and Ullah A, Robustify financial time series forecasting with bagging, Econometric Reviews, 2014, 33: 575–605.

    Article  MathSciNet  Google Scholar 

  51. Campbell J Y and Thompson S B, Predicting excess stock returns out of sample: Can anything beat the historical average? Review of Financial Studies, 2008, 21: 1509–1531.

    Article  Google Scholar 

  52. Angrist J D and Pischke J S, Mostly Harmless Econometrics: An Empiricist’s Companion, Princeton University Press, Princeton, 2009.

    Book  Google Scholar 

  53. Wooldridge J M, Introductory Econometrics, Thompson South-Western, South Burlington, 2003.

    Google Scholar 

  54. Zhang X, Yu D, Zou G, et al., Optimal model averaging estimation for generalized linear models and generalized linear mixed-effects model, Journal of the American Statistical Association, 2016, 111: 1775–1790.

    Article  MathSciNet  Google Scholar 

  55. Li K C, Asymptotic optimality for Cp, CL, cross-validation and generalized cross-validation: Discrete index set, Annals of Statistics, 1987, 15: 958–975.

    Article  MathSciNet  Google Scholar 

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Author information

Author notes

  1. These authors contributed equally: YOU Kang and WANG Miaomiao.

Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100089, China

    Kang You & Guohua Zou

  2. School of Chinese Materia Medica, Beijing University of Chinese Medicine, Beijing, 100105, China

    Miaomiao Wang

Authors
  1. Kang You
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  2. Miaomiao Wang
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  3. Guohua Zou
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Corresponding author

Correspondence to Guohua Zou.

Ethics declarations

The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11971323 and 12031016.

This paper was recommended for publication by Editor LIAO Jun.

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You, K., Wang, M. & Zou, G. Jackknife Model Averaging for Composite Quantile Regression. J Syst Sci Complex 37, 1604–1637 (2024). https://doi.org/10.1007/s11424-024-2448-1

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  • DOI: https://doi.org/10.1007/s11424-024-2448-1

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