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Asymptotic Expansions

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Mathematics for Econometrics

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Abstract

This chapter deals with situations in which we wish to approximate the limiting distribution of an estimator. As such it is different from other chapters in that it does not discuss topics in core econometrics and the ancillary mathematics needed to develop and fully understand them. Moreover, its purpose is different from that of the earlier (theoretical) chapters. Its aim is not only to introduce certain (additional) mathematical concepts but also to derive certain results that may prove useful for econometric applications involving hypothesis testing.

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Notes

  1. 1.

    Nearly all concepts contained in this chapter are being dealt in much greater detail elsewhere in this volume. We undertake this discussion only in order to make this chapter as self contained as possible for those who are familiar with the broad aspects of probability theory and do not wish to go through the more detailed expositions above.

  2. 2.

    Evidently, this is so only when moments of all orders exist. If, for example, the (n + 1)st moment does not exist, only the second bound is relevant.

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Authors and Affiliations

  1. Department of Economics, Columbia University, New York, USA

    Phoebus J. Dhrymes

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  1. Phoebus J. Dhrymes
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Dhrymes, P.J. (2013). Asymptotic Expansions. In: Mathematics for Econometrics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8145-4_13

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