Mathematical Underpinnings of Probability Theory
The purpose of this chapter is to provide a background on the results from probability and inference theory required for the study of several of the topics of contemporary econometrics.
An attempt will be made to give proofs for as many propositions as is consistent with the objectives of this chapter which are to provide the tools deemed necessary for the exposition of several topics in econometric theory; it is clearly not our objective to provide a substitute to a mathematical textbook of modern probability theory.
KeywordsMeasurable Function Lebesgue Measure Measure Space Inverse Image Finite Measure
- Anderson, T.W. and H. Rubin (1949), Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations, Annals of Mathematical Statistics, pp. 46–63.Google Scholar
- Anderson, T.W. and H. Rubin (1950), The Asymptotic Properties of Estimates of Parameters of in a Complete System of Stochastic Equations, Annals of Mathematical Statistics, pp. 570–582.Google Scholar
- Dhrymes, P. J. (1970). Econometrics: Statistical foundations and applications. New York: Harper and Row; also (1974). New York: Springer-Verlag.Google Scholar
- Dhrymes, P.J. (1982) Distributed Lags: Problems of Estmation and Formulation (corrected edition) Amsterdam: North HollandGoogle Scholar
- Kendall, M. G., & Stuart, A. (1963). The advanced theory of statistics. London: Charles Griffin.Google Scholar
- Sims, C.A. (1980). Macroeconomics and Reality, Econometrica, vol. 48, pp.1–48.Google Scholar
- Theil, H. (1953). Estimation and Simultaneous Correlation in Complete Equation Systems, mimeograph, The Hague: Central Plan Bureau.Google Scholar
- Theil, H. (1958). Economic Forecasts and Policy, Amsterdam: North Holland.Google Scholar