Abstract
The authors propose a V N, p test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed V N, p test statistic. Simulation results confirm that the proposed test performs satisfactorily in estimated size and power.
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H. J. Cui and S. X. Chen, Empirical likelihood confidence regions for parameter in the errors-in-variable models, Journal of Multivariate Analysis, 2003, 84(1): 101–115.
H. Liang, W. Härdle, and R. J. Carroll, Estimation in a semiparametric partially linear errors-in-variables model, The Annals of Statistics, 1999, 27(5): 1519–1535.
H. Liang, Asymptotic normality of parametric part in partially linear models with measurement error in the nonparametric part, Journal of Statistical Planning and Inference, 2000, 86(1): 51–62.
H. J. Cui and R. C. Li, On parameter estimation for semi-linear error-in-variable models, Journal of Multivariate Analysis, 1998, 64(1): 1–24.
H. J. Cui, Estimation in partially linear EV models with replicated observations, Science in China, Series A Mathematics, 2004, 47(1): 144–159.
T. J. Hastie and R. Tibshirani, Varying-coefficient models, Journal of the Royal Statistical Society, Series B, 1993, 55(5): 757–796.
Y. C. Xia and W. K. Li, On the estimation and testing of functional-coefficient linear models, Statistica Sinica, 1999, 9(4): 735–757.
J. Q. Fan and W. Zhang, Statistical estimation in varying coefficient models, The Annals of Statistics, 1999, 27(5): 1491–1518.
C. T. Chiang, A. R. John, and O. W. Colin, Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables, Journal of the American Statistical Association, 2002, 96(454): 605–619.
J. Z. Huang, C. O. Wu, and L. Zhou, Varying-coefficient model and biases function approximations for the analysis of repeated measurements, Biometrika, 2002, 89(1): 809–822.
J. Q. Fan and T. Huang, Profile likelihood inferences on semi-parametric varying-coefficient partially linear models, Bernoulli, 2005, 11(6): 1031–1057.
J. H. You and G. M. Chen, Estimation of a semiparametric varying-coefficient partially linear errors-in-variables model, Journal of Multivariate Analysis, 2006, 97(2): 324–341.
E. M. Chi and G. C. Reinsel, Models for longitudinal data with random effects and AR(1) errors, Journal of the American Statistical Association, 1989, 84(406): 452–459.
E. M. Chi and G. C. Reinsel, Asymptotic properties of the score test for autocorrelation in a random effects and AR(1) errors model, Statistics & Probability Letters, 1991, 11(5): 453–457.
E. Kyriazidou, Testing for serial correlation in multivariate regression models, Journal of Econometrics, 1998, 86(2): 193–220.
L. G. Godfrey, Alternative approaches to implementing Lagrange multiplier tests for serial correlation in dynamic regression models, Computational Statistics and Data Analysis, 2007, 57(7): 3282–3295.
Q. Li and C. Hsiao, Testing serial correlation in semiparametric panel data models, Journal of Econometrics, 1998, 87(2): 207–237.
D. D. Li and T. Stengos, Testing serial correlation in semi-parametric time series models, Journal of Time Series Analysis, 2003, 24(3): 311–335.
R. B. Gong, F Liu, J. Z. Zou, and M. Chen, Testing serial correlation in a linear EV model, Journal of Systems Science and Mathematical Sciences (in Chinese), 2007, 27(4): 510–520.
J. Durbin and G. S. Watson, Testing for serial correlation in least squares regression I, Biometrika, 1950, 37(3/4): 409–428.
J. Durbin and G. S.Watson, Testing for serial correlation in least squares regression Π, Biometrika, 1951, 38(1/2): 159–178.
T. S. Breusch, Testing for autocorrelation in dynamic linear models, Australian Economic Papers, 1978, 17(31): 334–355.
L. G. Godfrey, Testing for higher order serial correlation in regression equations when the regressors include lagged dependent variables, Econometrica, 1978, 46(6): 1303–1310.
J. T. Gao, Asymptotic theory for partly linear models, Communications in Statistic-Theory and Methods, 1995, 24(8): 1985–2010.
P. J. Brockwell and R. A. Davis, Times Series: Theory and Methods (Second Edition), Springer-Verlag, New York, 1991.
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This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003; the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609; the Doctor's Start-up Research Fund under Grant No. 08-52204; and the Youth Science Research Fund of Chongqing Technology and Business University under Grant No. 0852008.
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Hu, X., Liu, F. & Wang, Z. Testing serial correlation in semiparametric varying coefficient partially linear errors-in-variables model. J Syst Sci Complex 22, 483–494 (2009). https://doi.org/10.1007/s11424-009-9180-8
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DOI: https://doi.org/10.1007/s11424-009-9180-8