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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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  • Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
  • Handle: RePEc:eee:econom:v:110:y:2002:i:1:p:27-65
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    3. Erik Vogt, 2014. "Option-implied term structures," Staff Reports 706, Federal Reserve Bank of New York.
    4. Giuseppe De Luca & Valeria Perotti, 2011. "Estimation of ordered response models with sample selection," Stata Journal, StataCorp LP, vol. 11(2), pages 213-239, June.
    5. 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.
    6. 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.
    7. 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.
    8. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    9. Schwiebert, Jörg, 2012. "Analyzing the Composition of the Female Workforce - A Semiparametric Copula Approach," Hannover Economic Papers (HEP) dp-503, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    10. Gallant, A. Ronald & Tauchen, George, 2002. "Simulated Score Methods and Indirect Inference for Continuous-time Models," Working Papers 02-09, Duke University, Department of Economics.
    11. Ronald Gallant, A. & Tauchen, George, 2018. "Exact Bayesian moment based inference for the distribution of the small-time movements of an Itô semimartingale," Journal of Econometrics, Elsevier, vol. 205(1), pages 140-155.
    12. 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, September.
    13. 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.
    14. 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.
    15. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    16. Breunig, Christoph, 2021. "Varying random coefficient models," Journal of Econometrics, Elsevier, vol. 221(2), pages 381-408.
    17. Kevin Hasker & Robin Sickles, 2010. "eBay in the Economic Literature: Analysis of an Auction Marketplace," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 37(1), pages 3-42, August.
    18. Teruko Takada, 2001. "Nonparametric density estimation: A comparative study," Economics Bulletin, AccessEcon, vol. 3(16), pages 1-10.

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