Sowell, Fallaw (2006): The Empirical Saddlepoint Approximation for GMM Estimators.

PDF
MPRA_paper_3356.pdf Download (394kB)  Preview 
Abstract
The empirical saddlepoint distribution provides an approximation to the sampling distributions for the GMM parameter estimates and the statistics that test the overidentifying restrictions. The empirical saddlepoint distribution permits asymmetry, nonnormal tails, and multiple modes. If identification assumptions are satisfied, the empirical saddlepoint distribution converges to the familiar asymptotic normal distribution. In small sample Monte Carlo simulations, the empirical saddlepoint performs as well as, and often better than, the bootstrap.
The formulas necessary to transform the GMM moment conditions to the estimation equations needed for the saddlepoint approximation are provided. Unlike the absolute errors associated with the asymptotic normal distributions and the bootstrap, the empirical saddlepoint has a relative error. The relative error leads to a more accurate approximation, particularly in the tails.
Item Type:  MPRA Paper 

Institution:  Carnegie Mellon University 
Original Title:  The Empirical Saddlepoint Approximation for GMM Estimators 
Language:  English 
Keywords:  Generalized method of moments estimator; test of overidentifying restrictions; sampling distribution; empirical saddlepoint approximation; asymptotic distribution 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General 
Item ID:  3356 
Depositing User:  Fallaw Sowell 
Date Deposited:  30. May 2007 
Last Modified:  12. Feb 2013 18:34 
References:  Almudevar, Anthony, Chris Field and John Robinson (2000) "The Density of Multivariate MEstimates," The Annals of Statistics vol. 28, no. 1, pp. 275297. Amari, Shuichi (1985) DifferentialGeometrical Methods in Statistics, Berlin Heidelberg SpringerVerlag, Lecture Notes in Statistics, 28. Anatolyev, Stanislav (2005) "GMM, GEL, Serial Correlation, and Asymptotic Bias," Econometrica, vol. 73(3), pp. 9831002. Bhattacharya, R. N. and J. K. Ghosh (1978) "On the Validity of the Formal Edgeworth Expansion," Annals of Statistics vol 6, pp. 434451. Boothby, William M. (2003) An Introduction to Differentiable Manifolds and Riemannian Geometry, revised second edition, Academic Press. Daniels, H.E. (1954) "Saddlepoint approximations in statistics," Annals of Mathematical Statistics vol. 25, pp. 631650. Dominguez, M. A., and I. N. Lobato (2004) "Consistent Estimation of Models Defined by Conditional Moment Restrictions," Econometrica, vol. 72, pp. 16011615. Esscher, F. (1932) "The probability function in the collective theory of risk," Skand. Aktuarietidskr. Tidskr., vol. 15, pp. 175195. Feuerverger, Andrey (1989) "On the Empirical Saddlepoint Approximation," Biometrika vol. 76, pp. 457464. Field, C. A.(1982) "Small Sample Asymptotics for Multivariate MEstimates," Annals of Statistics, vol. 10, pp. 672689. Field, C. A. and E. Ronchetti (1990) Small Sample Asymptotics, Hayward, CA. IMS Monograph Series, vol 13. Goutis, Constantin and George Casella (1999) "Explaining the Saddlepoint Approximation," The American Statistician vol. 53, no. 3. pp. 216224. Hall, Peter and Joel L. Horowitz (1996) "Bootstrap Critical Values for Tests Based on GeneralizedMethodofMoments Estimators," Econometrica vol 64, no. 4, pp. 891916. Hansen, L.P. (1982) "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica vol. 50. Hansen, L.P., John Heaton, and A. Yaron (1996) "Finite Sample Properties of Some Alternative GMM Estimators," Journal of Business and Economic Statistics, vol. 14 no.3. Huzurbazar, S. (1999) "Practical Saddlepoint Approximations," The American Statistician, vol. 53, no. 3, pp. 225232. Jensen, J. L. (1995) Saddlepoint Approximations, Oxford University Press, Oxford. Kitamura, Yuichi and Michael Stutzer (1997) "An InformationTheoretic Alternative to Generalized Method of Moments Estimation," Econometrica vol. 65, no. 4, pp. 861874. Kolassa, J.E. (1997) Series Approximation Methods in Statistics, 2nd edition, New York, SpringerVerlag, Lecture Notes in Statistics, 88. Lugannani, R. and S. Rice (1980) "Saddle Point Approximations for the Distribution of the Sum of Independent Random Variables," Advances in Applied Probability vol. 12, pp. 475490. Marriott, Paul and Mark Salmon (2000) Applications of Differential Geometry to Econometrics, Cambridge, Cambridge University Press. Newey, Whitney and Richard J. Smith (2004) "Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators," Econometrica vol. 72, no. 1, pp. 219255. Phillips, P. C. B. (1978) "Edgeworth and Saddlepoint Approximations in the FirstOrder Noncircular Autoregression," Biometrika, 65, pp. 9198. Reid, N. (1988) "Saddlepoint Methods and Statistical Inference," {Statistical Science vol 3, no. 2, pp. 213227. Robinson, J. E. Ronchetti and G. A. Young (2003) "Saddlepoint Approximations and Tests based on Multivariate Mestimates," Annals of Statistics vol. 31, no. 4, pp. 11541169. Rochetti, Elvezio and Fabio Trojani (2003) "Saddlepoint Approximations and Test Statistics for Accurate Inference in Overidentified Moment Conditions Models," National Centre of Competence in Research Financial Valuation and Risk Management, working paper 27. Rochetti, Elvezio and A. H. Welsch (1994) "Empirical Saddlepoint Approximations for Multivariate MEstimators," Journal of the Royal Statistical Society, Series B, vol. 56, pp. 313326. Rilstone, Paul, V. K. Srivastava and Aman Ullah (1996) "The SecondOrder Bias and Mean Squared Error of Nonlinear Estimators," Journal of Econometrics, vol 75, pp. 369395. Skovgaard, I. M. (1990) "On the Density of minimum contrast estimators," Annals of Statistics, vol. 18, pp. 779789. Sowell, F. B. (1996) "Optimal Tests for Parameter Instability in the Generalized Method of Moments Framework," Econometrica vol. 64, no. 5. pp. 10851107. Stock, James and Jonathan Wright (2000) "GMM with Weak Identification," Econometrica, vol. 68(5), pp. 10551096. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/3356 