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Testing Serial Correlation in Partially Linear Additive Models

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Abstract

As an extension of partially linear models and additive models, partially linear additive model is useful in statistical modelling. This paper proposes an empirical likelihood based approach for testing serial correlation in this semiparametric model. The proposed test method can test not only zero first-order serial correlation, but also higher-order serial correlation. Under the null hypothesis of no serial correlation, the test statistic is shown to follow asymptotically a chi-square distribution. Furthermore, a simulation study is conducted to illustrate the performance of the proposed method.

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References

  1. Box, G.E.P., Pierce, D.A. Distribution of residual correlations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65: 1509–1526 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  2. Breusch, T.S., Pagan, A.R. The Lagrange multiplier test and its application to model specification in econometrics. Review of Economic Studies, 47: 239–254 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fan, J.Q., Jiang, J.C. Nonparametric inferences for additive models. J. Amer. Statist. Assoc., 100: 890–907 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Godfrey, L.G. Testing for higher order serial correlation in regression equations when the regressors include lagged dependent variables. Econometrica, 46: 1303–1310 (1978)

    Article  MATH  Google Scholar 

  5. Gao, J.T. Asymptotic theory for partly linear models. Commun. Statist. Theor. Meth., 24: 1985–2010 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hu, X.M., Wang, Z.Z, Liu, F. Testing serial correlation in semiparametric varying coefficient partially linear models. Commun. Statist. Theor. Meth., 3813): 2145–2163 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jiang, J., Zhou, H., Jiang, X., Peng, J. Generalized likelihood ratio tests for the structures of semiparametric additive models. The Canadian Journal of Statistics, 35: 381–398 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, D.D., Stengos, T. Testing serial correlation in semi-parametric time series models. J. Time Ser. Anal., 24: 311–335 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Li, Q. Efficient estimation of additive partially linear models. Internat. Econom. Rev., 41: 1073–1092 (2000)

    Article  MathSciNet  Google Scholar 

  10. Li, Q, Hsiao, C. Testing serial correlation in semiparametric panel data models. J. Econometrics, 87: 207–237 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liang, H., Thurston, H., Ruppert, D., Apanasovich, T. Additive partial linear models with measurement errors. Biometrika, 95: 667–678 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, F., Chen, G.M., Chen, M. Testing serial correlation in partial linear errors-in-variables models based on empirical likelihood. Commun. Statist. Theor. Meth., 3712): 1905–1918 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Liu, X., Wang, L., Liang, H. Estimation and variable selection for semiparametric additive partial linear model. Statistica Sinica, 213): 1225–1248 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ljung, G.M., Box, G.E.P. On a measure of lack of fit in time series models. Biometrika, 65: 297–303 (1978)

    Article  MATH  Google Scholar 

  15. Manzana, S., Zeromb, D. Kernel estimation of a partially linear additive model. Statistics and Probability Letters, 72: 313–322 (2005)

    Article  MathSciNet  Google Scholar 

  16. Opsomer, J.D., Ruppert, D. Fitting a bivariate additive model by local polynomial regression. Ann. Statist., 25: 186–211 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. Opsomer, J.D, Ruppert, D. A root-n consistent backfitting estimator for semiparametric additive modelling. J. Comput. Graph. Statist., 8: 715–732 (1999)

    Google Scholar 

  18. Owen, A.B. Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75: 237–249 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  19. Owen, A.B. Empirical likelihood ratio confidence regions. Ann. Statist., 18: 90–120 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  20. Owen, A.B. Empirical likelihood for linear models. Ann. Statist., 19: 1725–1747 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  21. Owen, A.B. Empirical Likelihood. Chapman and Hall, New York, 2001

    Book  MATH  Google Scholar 

  22. Wand, M.P. A central limit theorem for local polynomial backfitting estimators. Journal of Multivariate Analysis, 70: 57–65 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wei, C.H., Liu, C.L. Statistical inference on semiparametric partially linear additive models. Journal of Nonparametric Statistics, 24: 809–823 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Wei, C.H., Wang, X.N. Liu-type estimator in semiparametric partially linear additive models. Journal of Nonparametric Statistics, 283): 459–468 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Editor and referees for their truly helpful comments and suggestions which led to a much improved presentation.

Author information

Authors and Affiliations

  1. School of Statistics and Data Science, Nankai University, Tianjin, 300071, China

    Jin Yang

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    Jin Yang

  3. Department of Statistics, School of Science, Minzu University of China, Beijing, 100081, China

    Chuan-hua Wei

Authors
  1. Jin Yang
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  2. Chuan-hua Wei
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Corresponding author

Correspondence to Chuan-hua Wei.

Additional information

Chuanhua Wei’s research was supported by the National Natural Science Foundation of China (11301565), Jin Yang’s research was supported by the Post-doctoral Fellowship of Nankai University.

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Yang, J., Wei, Ch. Testing Serial Correlation in Partially Linear Additive Models. Acta Math. Appl. Sin. Engl. Ser. 35, 401–411 (2019). https://doi.org/10.1007/s10255-019-0808-8

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  • DOI: https://doi.org/10.1007/s10255-019-0808-8

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