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Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters

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  • Fan, Yanqin
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    Abstract

    In this paper, we study the bias-corrected test developed in Fan (1994). It is based on the integrated squared difference between a kernel estimator of the unknown density function of a random vector and a kernel smoothed estimator of the parametric density function to be tested under the null hypothesis. We provide an alternative asymptotic approximation of the finite-sample distribution of this test by fixing the smoothing parameter. In contrast to the normal approximation obtained in Fan (1994) in which the smoothing parameter shrinks to zero as the sample size grows to infinity, we obtain a non-normal asymptotic distribution for the bias-corrected test. A parametric bootstrap procedure is proposed to approximate the critical values of this test. We show both analytically and by simulation that the proposed bootstrap procedure works. Consistency and local power properties of the bias-corrected test with a fixed smoothing parameter are also discussed.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 14 (1998)
    Issue (Month): 05 (October)
    Pages: 604-621

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    Handle: RePEc:cup:etheor:v:14:y:1998:i:05:p:604-621_14

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    Cited by:
    1. Qi Li & Esfandiar Maasoumi & Jeffrey S. Racine, 2008. "A Nonparametric Test for Equality of Distributions with Mixed Categorical and Continuous Data," Emory Economics 0805, Department of Economics, Emory University (Atlanta).
    2. George Kapetanios & Tony Yates, 2014. "Evolving UK and US macroeconomic dynamics through the lens of a model of deterministic structural change," Empirical Economics, Springer, vol. 47(1), pages 305-345, August.
    3. Jiménez Gamero, M.D. & Muñoz García, J. & Pino Mejías, R., 2005. "Testing goodness of fit for the distribution of errors in multivariate linear models," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 301-322, August.
    4. Ot�vio Bartalotti, 2013. "Theory and Practice of Inference in Regression Discontinuity: A Fixed-Bandwidth Asymptotics Approach," Working Papers 1302, Tulane University, Department of Economics, revised Nov 2013.
    5. Alba Fernández, V. & Jiménez Gamero, M.D. & Muñoz Garcia, J., 2008. "A test for the two-sample problem based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3730-3748, March.
    6. Olivier Scaillet, 2005. "Kernel Based Goodness-of-Fit Tests for Copulas with Fixed Smoothing Parameters," FAME Research Paper Series rp145, International Center for Financial Asset Management and Engineering.
    7. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    8. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    9. Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
    10. Lin, Liang-Ching & Lee, Sangyeol & Guo, Meihui, 2013. "Goodness-of-fit test for stochastic volatility models," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 473-498.
    11. Hsu, Shih-Hsun & Kuan, Chung-Ming, 2014. "Constructing smooth tests without estimating the eigenpairs of the limiting process," Journal of Econometrics, Elsevier, vol. 178(P1), pages 71-79.
    12. Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.
    13. Kapetanios, George & Yates, Tony, 2011. "Evolving UK and US macroeconomic dynamics through the lens of a model of deterministic structural change," Bank of England working papers 434, Bank of England.
    14. Kapetanios, George, 2008. "Bootstrap-based tests for deterministic time-varying coefficients in regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 534-545, December.
    15. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.

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