IDEAS home Printed from https://ideas.repec.org/a/sae/sagope/v5y2015i1p2158244015575555.html
   My bibliography  Save this article

Least Squared Simulated Errors

Author

Listed:
  • Peter J. Veazie
  • Shubing Cai

Abstract

Estimation by minimizing the sum of squared residuals is a common method for parameters of regression functions; however, regression functions are not always known or of interest. Maximizing the likelihood function is an alternative if a distribution can be properly specified. However, cases can arise in which a regression function is not known, no additional moment conditions are indicated, and we have a distribution for the random quantities, but maximum likelihood estimation is difficult to implement. In this article, we present the least squared simulated errors (LSSE) estimator for such cases. The conditions for consistency and asymptotic normality are given. Finite sample properties are investigated via Monte Carlo experiments on two examples. Results suggest LSSE can perform well in finite samples. We discuss the estimator’s limitations and conclude that the estimator is a viable option. We recommend Monte Carlo investigation of any given model to judge bias for a particular finite sample size of interest and discern whether asymptotic approximations or resampling techniques are preferable for the construction of tests or confidence intervals.

Suggested Citation

  • Peter J. Veazie & Shubing Cai, 2015. "Least Squared Simulated Errors," SAGE Open, , vol. 5(1), pages 21582440155, March.
    • Handle: RePEc:sae:sagope:v:5:y:2015:i:1:p:2158244015575555
    DOI: 10.1177/2158244015575555
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/2158244015575555
    Download Restriction: no
    File URL: https://libkey.io/10.1177/2158244015575555?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    2. Gourieroux, Christian & Monfort, Alain, 1993. "Simulation-based inference : A survey with special reference to panel data models," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 5-33, September.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    4. Clarke, Kevin A., 2007. "A Simple Distribution-Free Test for Nonnested Model Selection," Political Analysis, Cambridge University Press, vol. 15(3), pages 347-363, July.
    5. Hess, Stephane & Train, Kenneth E. & Polak, John W., 2006. "On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 147-163, February.
    6. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
    7. Steven Stern, 1997. "Simulation-Based Estimation," Journal of Economic Literature, American Economic Association, vol. 35(4), pages 2006-2039, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Heiss, Florian & Winschel, Viktor, 2006. "Estimation with Numerical Integration on Sparse Grids," Discussion Papers in Economics 916, University of Munich, Department of Economics.
    2. Victor Aguirregabiria & Arvind Magesan, 2013. "Euler Equations for the Estimation of Dynamic Discrete Choice Structural Models," Advances in Econometrics, in: Structural Econometric Models, volume 31, pages 3-44, Emerald Group Publishing Limited.
    3. Aguirregabiria, Victor & Magesan, Arvind, 2013. "Euler Equations for the Estimation of Dynamic Discrete Choice Structural," MPRA Paper 46056, University Library of Munich, Germany.
    4. Maruyama, Shiko, 2014. "Estimation of finite sequential games," Journal of Econometrics, Elsevier, vol. 178(2), pages 716-726.
    5. Peter Haan, 2005. "State Dependence and Female Labor Supply in Germany: The Extensive and the Intensive Margin," Discussion Papers of DIW Berlin 538, DIW Berlin, German Institute for Economic Research.
    6. Lee, Lung-Fei, 1997. "Simulated maximum likelihood estimation of dynamic discrete choice statistical models some Monte Carlo results," Journal of Econometrics, Elsevier, vol. 82(1), pages 1-35.
    7. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    8. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    9. Mesa-Arango, Rodrigo & Ukkusuri, Satish V., 2014. "Attributes driving the selection of trucking services and the quantification of the shipper’s willingness to pay," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 142-158.
    10. Marco A. Palma & Dmitry V. Vedenov & David Bessler, 2020. "The order of variables, simulation noise, and accuracy of mixed logit estimates," Empirical Economics, Springer, vol. 58(5), pages 2049-2083, May.
    11. Inkmann, Joachim, 2000. "Misspecified heteroskedasticity in the panel probit model: A small sample comparison of GMM and SML estimators," Journal of Econometrics, Elsevier, vol. 97(2), pages 227-259, August.
    12. Islam, Mouyid, 2015. "Multi-Vehicle Crashes Involving Large Trucks: A Random Parameter Discrete Outcome Modeling Approach," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 54(1).
    13. Train, Kenneth & Wilson, Wesley W., 2008. "Estimation on stated-preference experiments constructed from revealed-preference choices," Transportation Research Part B: Methodological, Elsevier, vol. 42(3), pages 191-203, March.
    14. Mohammed H. Alemu & Søren B. Olsen, 2017. "Can a Repeated Opt-Out Reminder remove hypothetical bias in discrete choice experiments? An application to consumer valuation of novel food products," IFRO Working Paper 2017/05, University of Copenhagen, Department of Food and Resource Economics.
    15. Sándor, Zsolt & Train, Kenneth, 2004. "Quasi-random simulation of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 313-327, May.
    16. Anna Conte & Peter G Moffatt & Mary Riddel, 2019. "The Multivariate Random Preference Estimatorfor Switching Multiple Price List Data," University of East Anglia School of Economics Working Paper Series 2019-04, School of Economics, University of East Anglia, Norwich, UK..
    17. de Lapparent, M., & Axhausen , K.W. & Frei, A., 2013. "Long distance mode choice and distributions of values of travel time savings in three European countries," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 53, pages 1-7.
    18. Andrén, Daniela & Andrén, Thomas, 2013. "State dependence in Swedish social assistance," Working Papers 2013:7, Örebro University, School of Business.
    19. Lee, Donghoon & Song, Kyungchul, 2015. "Simulated maximum likelihood estimation for discrete choices using transformed simulated frequencies," Journal of Econometrics, Elsevier, vol. 187(1), pages 131-153.
    20. Cherchi, Elisabetta & Guevara, Cristian Angelo, 2012. "A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 321-332.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:sagope:v:5:y:2015:i:1:p:2158244015575555. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.