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Empirical likelihood based diagnostics for heteroscedasticity in partial linear models

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  • Wong, Heung
  • Liu, Feng
  • Chen, Min
  • Ip, Wai Cheung

Abstract

In this paper, we propose a diagnostic technique for checking heteroscedasticity based on empirical likelihood for the partial linear models. We construct an empirical likelihood ratio test for heteroscedasticity. Also, under mild conditions, a nonparametric version of Wilk's theorem is derived, which says that our proposed test has an asymptotic chi-square distribution. Simulation results reveal that the finite sample performance of our proposed test is satisfactory in both size and power. An empirical likelihood bootstrap simulation is also conducted to overcome the size distortion in small sample sizes.

Suggested Citation

  • Wong, Heung & Liu, Feng & Chen, Min & Ip, Wai Cheung, 2009. "Empirical likelihood based diagnostics for heteroscedasticity in partial linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3466-3477, July.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:9:p:3466-3477
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    References listed on IDEAS

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    1. Qi-Hua Wang & Bing-Yi Jing, 2003. "Empirical likelihood for partial linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 585-595, September.
    2. Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
    3. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    4. Gao, Jiti, 1994. "Asymptotic theory for partly linear models," MPRA Paper 40452, University Library of Munich, Germany, revised 02 Dec 1994.
    5. Diblasi, Angela & Bowman, Adrian, 1997. "Testing for constant variance in a linear model," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 95-103, April.
    6. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-517, October.
    7. You, Jinhong & Chen, Gemai, 2005. "Testing heteroscedasticity in partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 61-70, June.
    8. Wang, Qi-Hua & Jing, Bing-Yi, 1999. "Empirical likelihood for partial linear models with fixed designs," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 425-433, February.
    9. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.

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