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Nonparametric Regression with Nonparametrically Generated Covariates

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  • Enno Mammen
  • Christoph Rothe
  • Melanie Schienle

Abstract

We analyze the properties of non- and semiparametric estimation procedures involving nonparametric regression with generated covariates. Such estimators appear in numerous econometric applications, including nonparametric estimation of simultaneous equation models, sample selection models, treatment effect models, and censored regression models, but so far there seems to be no unified theory to establish their statistical properties. Our paper provides such results, allowing to establish asymptotic properties like rates of consistency or asymptotic normality for a wide range of semi- and nonparametric estimators. We also show how to account for the presence of nonparametrically generated regressors when computing standard errors.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2010-059.

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Length: 48 pages
Date of creation: Dec 2010
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2010-059

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Keywords: Empirical Process; Propensity Score; Control Variable Methods; Semiparametric Estimation;

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References

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  1. Michael C. Burda & Mark Weder, 2010. "Payroll Taxes, Social Insurance and Business Cycles," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-042, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Hautsch, Nikolaus & Hess, Dieter E. & Veredas, David, 2010. "The impact of macroeconomic news on quote adjustments, noise, and informational volatility," CFS Working Paper Series, Center for Financial Studies (CFS) 2010/01, Center for Financial Studies (CFS).
  3. Christian Basteck & Tijmen R. Daniëls & Frank Heinemann, 2010. "Characterising Equilibrium Selection in Global Games with Strategic Complementarities," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Ulrich Horst & Traian A. Pirvu & Gonçalo Dos Reis, 2010. "On Securitization, Market Completion and Equilibrium Risk Transfer," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Johanna Kappus & Markus Reiß, 2011. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2011-027, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3774-3792.
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  10. Hautsch, Nikolaus & Malec, Peter & Schienle, Melanie, 2011. "Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes," CFS Working Paper Series, Center for Financial Studies (CFS) 2011/25, Center for Financial Studies (CFS).
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  17. Wolfgang Karl Härdle & Rainer Schulz & Weining Wang, 2010. "Prognose mit nichtparametrischen Verfahren," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  18. Thomas Post & Katja Hanewald, 2010. "Stochastic Mortality, Subjective Survival Expectations, and Individual Saving Behavior," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  19. Wolfgang Karl Härdle & Elena Silyakova, 2010. "Volatility Investing with Variance Swaps," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  20. Wolfgang Karl Härdle & Yarema Okhrin & Weining Wang, 2010. "Uniform confidence bands for pricing kernels," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  21. Ulrich Horst & Felix Naujokat, 2010. "Illiquidity and Derivative Valuation," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  22. Ulrich Horst & Santiago Moreno-Bromberg, 2010. "Efficiency and Equilibria in Games of Optimal Derivative Design," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  23. Schmidt, Sandra & Nautz, Dieter, 2010. "Why do financial market experts misperceive future monetary policy decisions?," ZEW Discussion Papers, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research 10-045, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  24. Maria Grith & Wolfgang Karl Härdle & Melanie Schienle, 2010. "Nonparametric Estimation of Risk-Neutral Densities," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  25. Juliane Scheffel, 2010. "Honey, I’ll Be Working Late Tonight. The Effect of Individual Work Routines on Leisure Time Synchronization of Couples," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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Citations

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Cited by:
  1. Enno Mammen & Christoph Rothe & Melanie Schienle, 2011. "Semiparametric Estimation with Generated Covariates," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2011-064, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Debopam Bhattacharya & Shin Kanaya & Margaret Stevens, 2012. "Are University Admissions Academically Fair?," Economics Series Working Papers, University of Oxford, Department of Economics 608, University of Oxford, Department of Economics.
  3. Jinyong Hahn & Geert Ridder, 2010. "The Asymptotic Variance of Semi-parametric Estimators with Generated Regressors," Textos para discussão, Department of Economics PUC-Rio (Brazil) 575, Department of Economics PUC-Rio (Brazil).
  4. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers, University of Oxford, Department of Economics 706, University of Oxford, Department of Economics.
  5. Nianqing Liu & Quang Vuong & Haiqing Xu, 2012. "Rationalization and Identification of Discrete Games with Correlated Types," Department of Economics Working Papers, The University of Texas at Austin, Department of Economics 130915, The University of Texas at Austin, Department of Economics.
  6. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
  7. Van Keilegom, Ingrid & Vanhems, Anne, 2011. "Semiparametric transformation model with endogeneity: a control function approach," TSE Working Papers, Toulouse School of Economics (TSE) 11-243, Toulouse School of Economics (TSE).
  8. Enno Mammen & Byeong U. Park & Melanie Schienle, 2012. "Additive Models: Extensions and Related Models," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2012-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Enno Mammen & Christoph Rothe & Melanie Schienle, 2012. "Generated Covariates in Nonparametric Estimation: A Short Review," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2012-042, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. Patrick W Saart & Jiti Gao & Nam Hyun Kim, 2014. "Econometric Time Series Specification Testing in a Class of Multiplicative Error Models," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 1/14, Monash University, Department of Econometrics and Business Statistics.

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