Asymptotic Theory

An Asymptotic Theory is the study of asymptotic expansions.

• AKA: Large-Sample Theory.
• See: Asymptotic Distribution, Prime Number Theorem, Mellin Transform, Mathematics, Statistics, Asymptotic Distribution, Asymptotic, Asymptote, Time Series, Henri Poincaré, Asymptotic Scale, Asymptotic Analysis, Big O Notation, Taylor Series.

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Asymptotic_theory Retrieved:2017-5-21.
  • Asymptotic theory or large-sample theory is the branch of mathematics which studies asymptotic expansions.

    An example of an asymptotic result is the prime number theorem:

    Let π(x) be the number of prime numbers that are smaller than or equal to x.

    Then the limit : [math]\displaystyle{ \lim_{x\rightarrow\infty}\frac{\pi(x)\ln(x)}{x} }[/math] exists, and it is equal to 1.

    Asymptotic theory ("asymptotics") is used in several mathematical sciences. In statistics, asymptotic theory provides limiting approximations of the probability distribution of sample statistics, such as the likelihood ratio statistic and the expected value of the deviance. Asymptotic theory does not provide a method of evaluating the finite-sample distributions of sample statistics, however. Non-asymptotic bounds are provided by methods of approximation theory.

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