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Introduction to the Mathematical and Statistical Foundations of Econometrics

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  • Bierens,Herman J.

Abstract

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.

Suggested Citation

  • Bierens,Herman J., 2005. "Introduction to the Mathematical and Statistical Foundations of Econometrics," Cambridge Books, Cambridge University Press, number 9780521542241.
    • Handle: RePEc:cup:cbooks:9780521542241
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    Cited by:

    1. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    2. Kenneth L. Sørensen & Rune Vejlin, 2014. "Return To Experience And Initial Wage Level: Do Low Wage Workers Catch Up?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(6), pages 984-1006, September.
    3. Simone Cerreia-Vioglio & Fulvio Ortu & Federico Severino & Claudio Tebaldi, 2023. "Multivariate Wold decompositions: a Hilbert A-module approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 45-96, June.
    4. Hanck, Christoph, 2006. "The Error-in-Rejection Probability of Meta-Analytic Panel Tests," Technical Reports 2006,46, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Huang, Bin & Wang, Qihua, 2010. "Semiparametric analysis based on weighted estimating equations for transformation models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2078-2090, October.
    6. Christoph Hanck, 2009. "Cross-sectional correlation robust tests for panel cointegration," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(7), pages 817-833.
    7. Dahl, Christian M. & Levine, Michael, 2006. "Nonparametric estimation of volatility models with serially dependent innovations," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 2007-2016, December.
    8. Hanck, Christoph, 2006. "Cross-Sectional Correlation Robust Tests for Panel Cointegration," Technical Reports 2006,44, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Bravo-Ureta, Boris E. & Cocchi, Horacio & Solís, Daniel, 2006. "Output Diversification among Small-Scale Hillside Farmers in El Salvador," IDB Publications (Working Papers) 3012, Inter-American Development Bank.
    10. Marius PETRESCU & Ionica ONCIOIU & Anca-Gabriela PETRESCU & Florentina-Raluca BÎLCAN & Mihai PETRESCU & Dumitru-Alexandru STOICA, 2021. "Estimating the Dynamics of Household Waste Management in Turkey," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 129-143, June.
    11. Guy Kaplanski & Haim Levy, 2012. "Executive Short-Term Incentive, Risk-Taking And Leverage-Neutral Incentive Scheme," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-45.

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