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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 article, the authors present the exact maximum likelihood estimator of the semi-Markov kernel, which governs the evolution of the SMC, and study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time.
Abstract: This article concerns maximum-likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum-likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain (SMC). We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time, when the number of copies tends to infinity. In both cases, we obtain strong consistency, asymptotic normality, and asymptotic efficiency for every finite dimensional vector of this estimator. Finally, we obtain explicit forms for the covariance matrices of the asymptotic distributions.

16 citations

Journal ArticleDOI
TL;DR: In this paper, the rank tests of symmetry when samples are drawn from purely discrete distributions so that ties of zero and non-zero observations may occur are considered in the same way as nonzero ones.
Abstract: The paper deals with problems of rank tests of symmetry when samples are drawn from purely discrete distributions so that ties of zero and non-zero observations may occur. Zero observations are considered in the same way as nonzero ones. Two ways of treatment of ties are used in the paper, randomization of ties and the method of averaged scores. The asymptotic distributions of the statistics are derived under hypothesis of symmetry and under contiguous alternatives of location. The asymptotic power and efficiency of tests are established.

16 citations

Journal ArticleDOI
TL;DR: In this article, the authors discuss the importance of the asymptotic distribution of estimators in the context of small sample properties and apply it to their findings on the magnitudes and directions of the "biases" observed in Ordinary Least Squares estimates for their system.
Abstract: The theme of the volume is doggedly operational. In effect, one is encouraged to formulate each Econometric problem precisely as dictated by the requisite Economic Theory, and solve the resultant estimation problem directly, by numerically maximizing the relevant likelihood function, thus eschewing approximations of unknown magnitude and importance. The finite sample behaviour of the adopted estimator can then be simulated to provide evidence on the reliability of the empirical results. In this rather novel methodology, the large body of established theory on the asymptotic distributions of estimators is assigned a limited role and merits discussion in but one chapter. "The small sample problem stems from the fact that asymptotic results provide no clear guide to finite sample distributions" (p. 219), although ". . . one would like to know how large is 'large"' (p. 76). Agreed, and specifically investigating this should surely be an important objective of experimental work on small-sample properties. However, comparisons with asymptotic results materialize only for situations in which the Maximum Likelihood Estimator is believed consistent and asymptotically efficient, even though Goldfeld and Quandt (G-Q below) consider a most commendable number of examples of mis-specified models or incorrect estimator choices. One of the main purposes of this review article is to indicate how valuable asymptotic theory can be in clarifying simulation work by applying it to their findings on the magnitudes and directions of the "biases" observed in Ordinary Least Squares estimates for their system

16 citations


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