Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference

Nickl, Richard and Pötscher, Benedikt M. (2009): Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference.

Abstract

Given a random sample from a parametric model, we show how indirect inference estimators based on appropriate nonparametric density estimators (i.e., simulation-based minimum distance estimators) can be constructed that, under mild assumptions, are asymptotically normal with variance-covarince matrix equal to the Cramér-Rao bound.

• Item Type: MPRA Paper
• Language: English
• Keywords: Simulation-based minimum distance estimation, indirect inference
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Adams, R. A. & J. J. F. Fournier (2003): Sobolev Spaces. 2nd edition, Elsevier.

Altissimo, F. & A. Mele (2009): Simulated nonparametric estimation of dynamic models. Review of Economic Studies, forthcoming.

Beran, R. (1977): Minimum Hellinger distance estimates for parametric models. Annals of Statistics 5, 445-463.

Bickel, P. & Y. Ritov (2003): Nonparametric estimators that can be `plugged-in'. Annals of Statistics 31, 1033-1053.

Carrasco, M., M. Chernov, J. P. Florens & E. Ghysels (2007): Efficient estimation of general dynamic models with a continuum of moment conditions. Journal of Econometrics 140, 529-573.

DeVore, R. A. & G. G. Lorentz (1993): Constructive Approximation. Springer-Verlag.

Donoho, D. L. & R. C. Liu (1988): The "automatic" robustness of minimum distance functionals. Annals of Statistics 16, 552-586.

Fermanian, J. D. & B. Salanié (2004): A nonparametric simulated maximum likelihood estimation method. Econometric Theory 20, 701-734.

Folland, G. (1999): Real Analysis: Modern Techniques and Their Applications, 2nd edition, Wiley.

Gach, F. (2009): Efficiency in Indirect Inference. PhD Thesis, University of Vienna.

Gallant, R. & G. Tauchen (1996): Which moments to match? Econometric Theory 12, 657-681.

Gallant R. & J. Long (1997): Estimating stochastic differential equations efficiently by minimum chi-squared. Biometrika 84, 125-141.

Giné, E. & V. Koltchinskii (2006): Concentration inequalities and asymptotic results for ratio type empirical processes. Annals of Probability 34, 1143-1216.

Giné, E., R. Latała & J. Zinn (2000): Exponential and moment inequalities for U-statistics. In: Giné, E., Mason, D. M., Wellner, J. A. (eds.): High-dimensional Probability II, Progress in Probability 47, 13-38.

Giné, E. & R. Nickl (2008): Uniform central limit theorems for kernel density estimators. Probability Theory and Related Fields 141, 333-387.

Giné, E. & R. Nickl (2009a): An exponential inequality for the distribution function of the kernel density estimator, with applications to adaptive estimation. Probability Theory and Related Fields, forthcoming.

Giné, E. & R. Nickl (2009b): Uniform limit theorems for wavelet density estimators. Annals of Probability, forthcoming.

Gourieroux, C., A. Monfort, & E. Renault (1993): Indirect inference. Journal of Applied Econometrics 8, 85-118.

Gourieroux, C. & A. Monfort (1996): Simulation-based econometric methods. Oxford University Press.

Huber, P. J. (1972): Robust statistics: A review. Annals of Mathematical Statistics 43, 1041-1067.

Jiang, W. & B. Turnbull (2004): The indirect method: Inference based on intermediate statistics -- A synthesis and examples. Statistical Science 19, 239-263.

Lindsay (1994): Efficiency versus robustness: The case for minimum Hellinger distance and related methods. Annals of Statistics 22, 1081-1114.

Lorentz, G. G., v.Golitschek, M. & Y. Makovoz (1996): Constructive Approximation: Advanced Problems. Springer-Verlag.

Millar, P. W. (1981): Robust estimation via minimum distance methods. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 55, 73-89.

Nickl, R. (2007): Donsker-type theorems for nonparametric maximum likelihood estimators. Probability Theory and Related Fields 138, 411-449.

Pötscher, B. M. & I. R. Prucha (1997): Dynamic Nonlinear Econometric Models: Asymptotic Theory. Springer-Verlag.

Shadrin, A. Yu. (2001): The L_{∞}-norm of the L₂-spline projector is bounded independently of the knot sequence: a proof of de Boor's conjecture. Acta Mathematica 187, 59-137.

Smith, A. (1993): Estimating nonlinear time-series models using simulated vector autoregressions. Journal of Applied Econometrics 8, 63-84.

van der Vaart, A. W. & J. A. Wellner (1996): Weak Convergence and Empirical Processes With Applications to Statistics. Springer-Verlag.