Abstract
Central limit theorems describe the behaviour of distributions of sums of random variables. We start with the classical result of distributions of sums of independent random variables converging to the Gaussian (bell-curve) distribution. We describe the most important cases of convergence to Gaussian distributions (sums of martingale differences) as well as convergence to other distributions.
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Bibliography
Billingsley, P. 1995. Probability and measure. 3rd ed. New York: Wiley.
Billingsley, P. 1999. Convergence of probability measures. 2nd ed. New York: Wiley-Interscience.
Davidson, J. 1994. Stochastic limit theory: An introduction for econometricians. Oxford: Oxford University Press.
Hall, P., and C.C. Heyde. 1980. Martingale limit theory and its application. New York: Academic.
Hayashi, F. 2000. Econometrics. Princeton: Princeton University Press.
Ibragimov, I.A., and Yu.V. Linnik. 1971. Independent and stationary sequences of random variables. Groningen: Wolters-Noordhoff.
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Ploberger, W. (2018). Central Limit Theorems. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2628
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2628
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Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
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