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On the choice of regularization parameters in specification testing: a critical discussion

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Abstract

This article reviews and discusses the problem of choosing smoothing parameters and resampling schemes for specification tests in econometrics. While smoothing is used for the regularization of the non-specified parts of the null hypothesis and omnibus alternatives, the resampling serves for determining the critical value. Several of the existing selection methods are discussed, implemented, and compared. This has been done for cross-sectional data along the example of additivity testing. Doubtless, all problems considered here carry over to specification testing with dependent data. Intensive simulations illustrate that this is still an open problem that easily corrupts these tests in practice. Possible ways out of the dilemma are proposed.

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References

  • Barrientos J, Sperlich S (2010) The size problem of bootstrap tests when the null is non- or semiparametric. Revista Colombiana de Estadística 33:307–319

    Google Scholar 

  • Cao-Abad R (1993) Bootstrapping the mean integrated squared error. J Multivar Anal 45:137–160

    Article  Google Scholar 

  • Cao-Abad R, González-Manteiga W (1993) Bootstrap methods in regression smoothing. Nonparametr Stat 2:379–388

    Article  Google Scholar 

  • Chen SX, Gao J (2007) An adaptive empirical likelihood test for parametric time series regression models. J Econom 141:950–972

    Article  Google Scholar 

  • Claeskens G, Van Keilegom I (2003) Bootstrap confidence bands for regression curves and their derivatives. Ann Stat 6:1852–1884

    Google Scholar 

  • Davidson R, Flachaire E (2008) The wild bootstrap, tamed at last. J Econom 146:162–169

    Article  Google Scholar 

  • Delgado MA, Rodriguez-Poó JM, Wolf M (2001) Subsampling cube root asymptotics with an application to Manski’s MSE. Econ Lett 73:241–250

    Article  Google Scholar 

  • Dette H, von Lieres und Wilkau C, Sperlich S (2005) A comparison of different nonparametric method for inference on additive models. Nonparametr Stat 17:57–81

    Article  Google Scholar 

  • Duong T, Hazelton M (2003) Plug-in bandwidth matrices for bivariate kernel density estimation. Nonparametr Stat 15:7–30

    Google Scholar 

  • Eubank RL, Ching-Shang L, Wang S (2005) Testing lack of fit of parametric regression models using nonparametric regression techniques. Statistica Sinica 15:135–152

    Google Scholar 

  • Fahrmeir L, Kneib T, Lang S (2004) Penalized structured additive regression: a Bayesian perspective. Statistica Sinica 14:731–761

    Google Scholar 

  • Fahrmeir L, Kneib T, Konrath S (2010) Bayesian regularisation in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection. Stat Comput 20:203–219

    Article  Google Scholar 

  • Gao J, Gijbels I (2008) Bandwidth selection in nonparametric kernel testing. J Am Stat Assoc 484: 1584–1594

    Google Scholar 

  • Gao J, Gijbels I, Van Bellegem S (2008) Nonparametric simultaneous testing for structural breaks. J Econometr 143:123–142

    Article  Google Scholar 

  • González-Manteiga W, Martínez-Miranda MD, Pérez-González A (2004) The choice of smoothing parameter in nonparametric regression through wild bootstrap. Comput Stat Data Anal 47:487–515

    Article  Google Scholar 

  • González-Manteiga W, Crujeiras RM (2013) An updated review of goodness-of-fit tests for regression models. Test Forthcom 22:361–411

    Google Scholar 

  • Gozalo PL, Linton OB (2001) Testing additivity in generalized nonparametric regression models with estimated parameters. J Econometr 104:1–48

    Article  Google Scholar 

  • Guerre E, Lavergne P (2005) Data-driven rate-optimal specification testing in regression models. Ann Stat 33:840–870

    Article  Google Scholar 

  • Härdle W, Mammen E (1993) Comparing nonparametric versus parametric regression fits. Ann Stat 21:1926–1947

    Article  Google Scholar 

  • Härdle W, Marron JS (1991) Bootstrap simultaneous bars for nonparametric regression. Ann Stat 19: 778–796

    Google Scholar 

  • Hart JD (1997) Nonparametric smoothing and lack-of-fit tests. Springer, New York

    Book  Google Scholar 

  • Hastie TJ, Tibshirani RJ (1990) Generalized additive models. Chapman & Hall, London

    Google Scholar 

  • Hengartner NW, Sperlich S (2005) Rate optimal estimation with the integration method in the presence of many covariates. J Multivar Anal 95:246–272

    Article  Google Scholar 

  • Horowitz JL, Spokoiny V (2001) An adaptive, rate-optimal test of parametric mean-regression model against a nonparametric alternative. Econometrica 69:599–631

    Article  Google Scholar 

  • Ibragimov IA, Khasminski RZ (1981) Statistical estimation; asymptotic theory. Springer, Heidelberg

    Book  Google Scholar 

  • Ingster YI (1982) Minimax nonparametric detection of signals in white Gaussian noise. Probl Inf Transm 18:130–140

    Google Scholar 

  • Ingster YI (1993) Asymptotically minimax hypothesis testing for nonparametric alternatives \(I, I\!I, I\!I\!I\). Math Methods Stat 2:85–114

    Google Scholar 

  • Jones MC, Davies SJ, Park BU (1994) Versions of kernel type regression estimators. J Am Stat Assoc 89:825–832

    Article  Google Scholar 

  • Kallenberg WCM, Ledwina T (1995) Consistency and Monte-Carlo simulations of a data driven version of smooth goodness-of-fit tests. Ann Stat 23:1594–1608

    Article  Google Scholar 

  • Kim W, Linton OB, Hengartner N (1999) A computationally efficient oracle estimator of additive nonparametric regression with bootstrap confidence intervals. J Comput Gr Stat 8:278–297

    Google Scholar 

  • Köhler M, Schindler A, Sperlich S (2013) A review and comparison of bandwidth selection methods for kernel regression. Int Stat Rev 74:215–233

    Google Scholar 

  • Kulasekera KB, Wang J (1997) Smoothing parameter selection for power optimality in testing of regression curves. J Am Stat Assoc 438:500–511

    Article  Google Scholar 

  • Ledwina T (1994) Data-driven version of Neyman’s smooth test of fit. J Am Stat Assoc 89:1000–1005

    Article  Google Scholar 

  • Linton OB, Nielsen JP (1995) A kernel method of estimating structured nonparametric regression based on marginal integration. Biometrika 82:93–101

    Article  Google Scholar 

  • Mammen E, Linton OB, Nielsen JP (1999) The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Ann Stat 27:1443–1490

    Google Scholar 

  • Mammen E, Park B (2005) Bandwidth selection for smooth backfitting in additive models. Ann Stat 33:1260–1294

    Article  Google Scholar 

  • Neumann MH, Polzehl J (1998) Simultaneous bootstrap confidence bands in nonparametric regression. J Nonparametr Stat 9:307–333

    Article  Google Scholar 

  • Neumeyer N, Sperlich S (2006) Comparison of separable components in different samples. Scand J Stat 33:477–501

    Article  Google Scholar 

  • Nielsen JP, Sperlich S (2005) Smooth backfitting in practice. J R Statl Soc B 67:43–61

    Article  Google Scholar 

  • Politis DN, Romano JP, Wolf M (1999) Subsampling. Springer series in statistics. Springer, Punta Gorda

    Google Scholar 

  • Roca-Pardiñas J, Sperlich S (2007) Testing the link when the index is semiparamtric: a comparison study. Comput Stat Data Anal 12:6565–6581

    Article  Google Scholar 

  • Rodriguez-Póo JM, Sperlich S, Vieu P (2012) And adaptive specification test for semiparametric models. Economet Theory 29:483–523

    Google Scholar 

  • Rosenblatt M (1969) Conditional probability density and regression estimators. Multivar Anal II:25–31

    Google Scholar 

  • Severance-Lossin E, Sperlich S (1999) Estimation of derivatives for additive separable models. Statistics 33:241–265

    Article  Google Scholar 

  • Sperlich S, Linton OB, Härdle W (1999) Integration and backfitting methods in additive models: finite sample properties and comparison. Test 8:419–458

    Article  Google Scholar 

  • Spokoiny V (1998) Adaptive and spatially adaptive testing of a nonparametric hypothesis. Math Methods Stat 7:245–273

    Google Scholar 

  • Su L, White H (2010) Testing structural change in partially linear models. Econometr Theory 26:1761–1806

    Article  Google Scholar 

  • Su L, Ullah A (2013) A nonparametric goodness-of-test-based test for conditional heteroskedasticity. Econometric Theory 29:187–212

    Google Scholar 

  • Su L, Tu Y, Ullah A (2013) Testing additive separability of error term in nonparametric structural models. Econometr Rev (forthcoming)

  • Su L, Murtazasvilli I, Ullah A (2013) Local linear GMM estimation of functional coefficient IV models with an application to estimating the rate of return to schooling. J Bus Econ Stat 31:184–207

    Google Scholar 

  • Vieu P (1993) Bandwidth selection for kernel regression: a survey. In: Härdle W, Simar L (ed) Computer intensive methods in statistics, statistics and computing 1, Physica, Berlin, pp 13–149

  • Wood SN (2008) Fast stable direct fitting and smoothness selection for generalized additive models. J R Stat Soc B 70:495–518

    Article  Google Scholar 

  • Zhang C (2003) Calibrating the degrees of freedom for automatic data smoothing and affective curve checking. J Am Stat Assoc 98:609–629

    Article  Google Scholar 

  • Zhang C (2004) Assessing the equivalence of nonparametric regression tests based on spline and local polynomial smoothers. J Stat Plan Inference 126:73–95

    Article  Google Scholar 

  • Zheng X (1996) A consistent test of a functional form via nonparametric estimation techniques. Journal of Econometrics 75:263–289

    Article  Google Scholar 

Download references

Acknowledgments

The author acknowledges the very helpful discussion of the anonymous referees and the editors, which has improved the paper a lot. Further thanks goes to Jorge Barrientos, Holger Dette, Juan Rodriguez-Poo, Vladimir Spokoiny, Michael Wolf, and the participants of the seminars at the Universities of Galicia, Spain. The author acknowledges funding from the Swiss National Science Foundation, project 100018-140295, and the Spanish MCyT, project MTM2008-03010.

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  1. Département des sciences économiques and Research Center for Statistics, Université de Genève, Bd du Pont d’Arve 40, 1211 , Geneva, Switzerland

    Stefan Sperlich

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  1. Stefan Sperlich
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Correspondence to Stefan Sperlich.

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Sperlich, S. On the choice of regularization parameters in specification testing: a critical discussion. Empir Econ 47, 427–450 (2014). https://doi.org/10.1007/s00181-013-0752-z

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