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Tests for p-regression Coefficients in Linear Panel Model When p is Divergent

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Abstract

This paper evaluates the performance of the FW-test for testing part of p-regression coefficients in linear panel data model when p is divergent. The asymptotic power of the FW-statistic is obtained under some regular conditions. The theoretical development are challenging since the number of covariates increases as the sample size increases. It is worth noting that the inference approach does not require any specification of the error distribution. Some simulation comparisons are conducted and show that the simulated power coincide with theoretical power well. The method is also illustrated using a renal cancer data example.

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References

  1. Arias-Castro E, Candès E J, Plan Y. Global testing under sparse alternatives: ANOVA, multiple comparisons and the higher criticism. The Annals of Statistics, 39: 2533–2556 (2011)

    Article  MathSciNet  Google Scholar 

  2. Bai, Z.D., Hewa Saranadasa. Effect of high dimension: by an example of a two sample problem. Statistica Sinica, 6: 311–329 (1996)

    MathSciNet  Google Scholar 

  3. Bai, Z.D., Yin, Y.Q. Limit of the smallest eigenvalue of a large dimensional sample covariance matrix. The Annals of Probability, 21: 1275–1294 (1993)

    Article  MathSciNet  Google Scholar 

  4. Baltagi, B. Econometrics Analysis of Panel Data. New York: Wiley Press, 2005

    Google Scholar 

  5. Bhansali, R.J., Giraitis, L., Kokoszka, P.S. Convergence of quadratic forms with nonvanishing diagonal. Statistics & probability letters, 77: 726–734 (2007)

    Article  MathSciNet  Google Scholar 

  6. Boni, J.P., Leister, C., Bender, G., Fitzpatrick, V., Twine, N., Stover, J., Dorner, A., Immermann, F., Burczynski, M.E. Population Pharmacokinetics of CCI-779: Correlations to Safety and Pharmacogenomic Responses in Patients with Advanced Renal Cancer. Clinical Pharmacology & Therapeutics, 77: 76–89 (2005)

    Article  Google Scholar 

  7. Cheng Hsiao. Analysis of panel data: Second Edition, Cambridge University Press, Cambridge, United Kingdom, 2003

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Fan, J., Feng, Y., Song, R. Nonparametric independence screening in sparse ultra-high dimensional additive models. Journal of the American Statistical Association, 106: 544–557 (2011)

    Article  MathSciNet  Google Scholar 

  10. Huang, J., Horowitz, J.L., Ma, S.G. Asymptotic properties of bridge estimators in sparse high-dimensional regression models. The Annals of Statistics, 36: 587–613 (2006)

    Article  MathSciNet  Google Scholar 

  11. Huang, J., Ma, S.G., Zhang, C.H. Adaptive LASSO for sparse highdimensional regression models. Statistica Sinica, 18: 1603–1618 (2008)

    MathSciNet  MATH  Google Scholar 

  12. Huang, J., Horowitz, J.L., Wei, F. Variable selection in nonparametric additive models. Annals of statistics, 38: 2282–2313 (2010)

    Article  MathSciNet  Google Scholar 

  13. Kosorok, M.R., Ma, S. Marginal asymptotics for the “large p, small n” paradigm: with applications to microarray data. The Annals of Statistics, 35: 1456–1486 (2007)

    Article  MathSciNet  Google Scholar 

  14. Peng, L., Qi, Y., Wang, R. Empirical likelihood test for high dimensional linear models. Statistics & Probability Letters, 86: 85–90 (2014)

    Article  MathSciNet  Google Scholar 

  15. Portnoy, S. Asymptotic behavior of the M-estimators of p-regression parameters when p2/n is large: normal approximation. The Annals of Statistics, 13: 1403–1417 (1985)

    Article  MathSciNet  Google Scholar 

  16. Portnoy, S. Asymptotic behavior of the M-estimators of p-regression parameters when p2/n is large: consistency. The Annals of Statistics, 12: 1298–1309 (1984)

    Article  MathSciNet  Google Scholar 

  17. Wang, S.Y., Cui, H.J. Generalized F test for high dimensional linear regression coefficients. Journal of Multivariate Analysis, 117: 134–149 (2013)

    Article  MathSciNet  Google Scholar 

  18. Wang, S.G., Ma, W.Q. On exact tests of linear hypothesis in linear models with nested error structure. Journal of Statistical Planning and Inference, 106: 225–233 (2002)

    Article  MathSciNet  Google Scholar 

  19. Wang, S.G., Shi, J.H., Yin, S.J., Wu, M.X. Introduction of Linear Models. Science Press, Beijing, 2004

    Google Scholar 

  20. Wang, L., Xue, L., Qu, A., Liang, H. Estimation and model selection in generalized additive partial linear models for correlated data with diverging number of covariates. Annals of Statistics, 42: 592–624 (2014)

    Article  MathSciNet  Google Scholar 

  21. Zhong, P.S., Chen, S.X. Tests for high dimensional regression coefficients with factorial designs. Journal of the American Statistical Association, 106: 260–274 (2011)

    Article  MathSciNet  Google Scholar 

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Correspondence to Wei-hu Cheng.

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This paper is supported by the National Key R&D Program of China (2016YFF0204205, 2017YFF0206503), the National Natural Science Foundation (Nos.11701021) and by the National Social Science Foundation of China (18BTJ021).

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Zhao, J., Wu, Mx., Cheng, Wh. et al. Tests for p-regression Coefficients in Linear Panel Model When p is Divergent. Acta Math. Appl. Sin. Engl. Ser. 36, 566–580 (2020). https://doi.org/10.1007/s10255-020-0947-y

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  • DOI: https://doi.org/10.1007/s10255-020-0947-y

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