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Dynamic Vector Mode Regression

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  • Kemp, GCR
  • Parente, PMDC
  • Santos Silva, JMC

Abstract

We study the semi-parametric estimation of the conditional mode of a random vector that has a continuous conditional joint density with a well-defined global mode. A novel full-system estimator is proposed and its asymptotic properties are studied allowing for possibly dependent data. We specifically consider the estimation of vector autoregressive conditional mode models and of structural systems of linear simultaneous equations definded by mode restrictions. The proposed estimator is easy to implement using standard software and the results of a small simulation study suggest that it is well behaved in finite samples.

Suggested Citation

  • Kemp, GCR & Parente, PMDC & Santos Silva, JMC, 2015. "Dynamic Vector Mode Regression," Economics Discussion Papers 13793, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:13793
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    References listed on IDEAS

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    1. Sakata, Shinichi, 2007. "Instrumental variable estimation based on conditional median restriction," Journal of Econometrics, Elsevier, vol. 141(2), pages 350-382, December.
    2. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    3. Lee, Myoung-jae, 1993. "Quadratic mode regression," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 1-19.
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    5. Muler, Nora & Yohai, V´ictor J., 2013. "Robust estimation for vector autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 68-79.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, January.
    7. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    8. Weixin Yao & Longhai Li, 2014. "A New Regression Model: Modal Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 656-671, September.
    9. Bernanke, Ben S., 1986. "Alternative explanations of the money-income correlation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 49-99, January.
    10. Krishnakumar, J. & Ronchetti, E., 1997. "Robust estimators for simultaneous equations models," Journal of Econometrics, Elsevier, vol. 78(2), pages 295-314, June.
    11. Galeano, Pedro & Pena, Daniel & Tsay, Ruey S., 2006. "Outlier Detection in Multivariate Time Series by Projection Pursuit," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 654-669, June.
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    Cited by:

    1. Timo Dimitriadis & Andrew J. Patton & Patrick W. Schmidt, 2019. "Testing Forecast Rationality for Measures of Central Tendency," Papers 1910.12545, arXiv.org, revised Jul 2024.
    2. Eduardo Schirmer Finn & Eduardo Horta, 2024. "Convolution Mode Regression," Papers 2412.05736, arXiv.org.
    3. Ullah, Aman & Wang, Tao & Yao, Weixin, 2023. "Semiparametric partially linear varying coefficient modal regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 1001-1026.
    4. Venables, Anthony J., 2017. "Breaking into tradables: Urban form and urban function in a developing city," Journal of Urban Economics, Elsevier, vol. 98(C), pages 88-97.
    5. Tao Wang, 2024. "Non‐parametric Estimator for Conditional Mode with Parametric Features," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(1), pages 44-73, February.
    6. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    7. Zhe Sun & Yundong Tu, 2024. "Factors in Fashion: Factor Analysis towards the Mode," Papers 2409.19287, arXiv.org.

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    Keywords

    Impulse response functions; Multivariate conditional mode; Robust regression; Simultaneous equations; Vector autoregression;
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