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Cross-validated SNP density estimates

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  • Coppejans, Mark
  • Gallant, A. Ronald

Abstract

We consider cross-validation strategies for the SNP nonparametric density estimator, which is a truncation (or sieve) estimator based upon a Hermite series expansion. Our main focus is on the use of SNP density estimators as an adjunct to EMM structural estimation. It is known that for this purpose a desirable truncation point occurs at the last point at which the MSE curve of the SNP density estimate declines abruptly. We study the determination of the MSE curve on a per sample basis for iid data by means of leave-one-out cross-validation and hold-out-sample cross-validation through an examination of their performance over the Marron-Wand test suite and models related to asset pricing and auction applications. We find that both methods are informative as to the location of abrupt drops. The hold-out-sample method is cheaper to compute because it requires fewer nonlinear optimizations. The minimum of the hold-out-sample cross-validation curve also seems to be a better indicator of the minimum of the true MSE curve. We consider the asymptotic justification of hold-out-sample cross-validation. For this purpose, we establish rates of convergence of the SNP estimator under the Hellinger norm that are of interest in their own right.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 110 (2002)
Issue (Month): 1 (September)
Pages: 27-65

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Handle: RePEc:eee:econom:v:110:y:2002:i:1:p:27-65

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Laffont, Jean-Jacques & Ossard, Herve & Vuong, Quang, 1995. "Econometrics of First-Price Auctions," Econometrica, Econometric Society, vol. 63(4), pages 953-80, July.
  2. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  3. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  4. A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 617-631, November.
  5. Alexander Michaelides & Serena Ng, 1997. "Estimating the Rational Expectations Model of Speculative Storage: A Monte Carlo Comparison of Three Simulation Estimators," Boston College Working Papers in Economics 373, Boston College Department of Economics.
  6. Chumacero Rómulo A., 1997. "Finite Sample Properties of the Efficient Method of Moments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(2), pages 1-19, July.
  7. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
  8. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
  9. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  10. Eastwood, Brian J. & Gallant, A. Ronald, 1991. "Adaptive Rules for Seminonparametric Estimators That Achieve Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 7(03), pages 307-340, September.
  11. Ronald Gallant, A. & Tauchen, George, 1999. "The relative efficiency of method of moments estimators1," Journal of Econometrics, Elsevier, vol. 92(1), pages 149-172, September.
  12. Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers 96-17, Duke University, Department of Economics.
  13. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  14. Gallant, A. Ronald & Souza, Geraldo, 1991. "On the asymptotic normality of Fourier flexible form estimates," Journal of Econometrics, Elsevier, vol. 50(3), pages 329-353, December.
  15. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  16. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
  17. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
  18. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
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Citations

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Cited by:
  1. Giuseppe De Luca & Valeria Perotti, 2010. "Estimation of ordered response models with sample selection," CEIS Research Paper 168, Tor Vergata University, CEIS, revised 03 Jun 2010.
  2. Giuseppe De Luca & Franco Peracchi, 2012. "Estimating Engel curves under unit and item nonresponse," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(7), pages 1076-1099, November.
  3. Valderrama, Diego, 2007. "Statistical nonlinearities in the business cycle: A challenge for the canonical RBC model," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 2957-2983, September.
  4. Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
  5. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  6. Schwiebert, Jörg, 2012. "Analyzing the Composition of the Female Workforce - A Semiparametric Copula Approach," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Leibniz Universität Hannover dp-503, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  7. Helena Veiga, 2007. "Are Feedback Factors Important in Modeling Financial Data?," International Review of Finance, International Review of Finance Ltd., vol. 7(3-4), pages 105-118.
  8. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
  9. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
  10. Kevin Hasker & Robin Sickles, 2010. "eBay in the Economic Literature: Analysis of an Auction Marketplace," Review of Industrial Organization, Springer, vol. 37(1), pages 3-42, August.
  11. Teruko Takada, 2001. "Nonparametric density estimation: A comparative study," Economics Bulletin, AccessEcon, vol. 3(16), pages 1-10.
  12. Chen, Xiaohong & Hong, Han & Shum, Matthew, 2007. "Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models," Journal of Econometrics, Elsevier, vol. 141(1), pages 109-140, November.

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