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Maximum likelihood estimation for Markov processes
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This article is published in Annals of the Institute of Statistical Mathematics.The article was published on 1972-12-01. It has received 18 citations till now. The article focuses on the topics: Maximum likelihood sequence estimation & Markov model.read more
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Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data
Andrew W. Lo,Andrew W. Lo +1 more
TL;DR: In this article, the authors considered the parametric estimation problem for continuous time stochastic processes described by general first-order nonlinear stochiastic differential equations of the Ito type and characterized the likelihood function of a discretely sampled set of observations as the solution to a functional partial differential equation.
Journal ArticleDOI
Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data
TL;DR: In this paper, the parametric estimation problem for continuous-time stochastic processes described by first-order nonlinear Stochastic Differential Equations of the generalized Ito type (containing both jump and diffusion components) is considered.
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Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator
TL;DR: In this paper, the authors extend Huber's results to the case of independent and identically distributed (i.i.n.d.) observations and show that the estimator O(n) is consistent and asymptotically normally distributed under weaker conditions than usual.
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Computation and Estimation of Generalized Entropy Rates for Denumerable Markov Chains
TL;DR: All the entropy rates of random sequences for general entropy functionals including the classical Shannon and Rényi entropies and the more recent Tsallis and Sharma-Mittal ones are shown to be either infinite or zero except at a threshold where they are equal to Shannon or Rênyi entropy rates up to a multiplicative constant.
Journal ArticleDOI
Asymptotic inference for stochastic processes
TL;DR: In this article, a survey of large-sample inference for stochastic processes is presented, where a unified framework is used to study the asymptotic properties of tests and estimators parameters in discrete-time, continuous-time jump-type, and diffusion processes.
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Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.
The behavior of maximum likelihood estimates under nonstandard conditions
TL;DR: In this paper, the authors prove consistency and asymptotic normality of maximum likelihood estimators under weaker conditions than usual, such that the true distribution underlying the observations belongs to the parametric family defining the estimator, and the regularity conditions do not involve the second and higher derivatives of the likelihood function.