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Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


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TL;DR: In this paper, the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein-Uhlenbeck process when a continuous record is available was obtained and an in-fill asymptotic theory for the least squares estimator was developed.
Abstract: This paper obtains the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein-Uhlenbeck process when a continuous record is available The exact distribution is asymmetric, tri-modal, dependent on the initial condition These three properties are also found in the finite sam- ple distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models Motivated by these observations, the paper then develops an in-fill asymptotic theory for the LS estimator of structural break point in the AR(1) coefficient The in-fill asymptotic distribution is also asymmetric, tri-modal, dependent on the initial condition, and delivers excellent approximations to the finite sample distribution Unlike the long-span asymptotic theory, which depends on the underlying AR root and hence is tailor-made but is only available in a rather limited number of cases, the in-fill asymptotic theory is continuous in the underlying roots Monte Carlo studies show that the in-fill asymptotic theory performs better than the long-span asymptotic theory for cases where the long-span theory is available and performs very well for cases where no long-span theory is available

13 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered a two-dimensional model Schrodinger equation with logarithmic integral non-linearity and found asymptotic expansions for its solutions (Airy polarons) that decay exponentially at the "semi-infinity" and oscillate along one direction.
Abstract: We consider a two-dimensional model Schrodinger equation with logarithmic integral non-linearity. We find asymptotic expansions for its solutions (Airy polarons) that decay exponentially at the "semi-infinity" and oscillate along one direction. These solutions may be regarded as new special functions, which are somewhat similar to the Airy function. We use them to construct global asymptotic solutions of Schrodinger equations with a small parameter and with integral non-linearity of Hartree type.

13 citations

Journal ArticleDOI
TL;DR: A short review of the various problems which arise in connection with the use of asymptotic methods in the optimal control of distributed systems is presented.

13 citations

Journal ArticleDOI
TL;DR: The asymptotic distribution of the least squares estimators in the random walk model was first found by White [17] and is described in terms of functional of Brownian motion with no closed form expression known as discussed by the authors.
Abstract: The asymptotic distribution of the least-squares estimators in the random walk model was first found by White [17] and is described in terms of functional of Brownian motion with no closed form expression known. Evans and Savin [5,6] and others have examined numerically both the asymptotic and finite sample distribution. The purpose of this paper is to derive an asymptotic expansion for the distribution. Our approach is in contrast to Phillips [12,13] who has already derived some terms in a general expansion by analyzing the functionals. We proceed by assuming that the errors are normally distributed and expand the characteristic function directly. Then, via numerical integration, we invert the characteristic function to find the distribution. The approximation is shown to be extremely accurate for all sample sizes ≥25, and can be used to construct simple tests for the presence of a unit root in a univariate time series model. This could have useful applications in applied economics.

12 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526