On Sequential Maximum Likelihood Estimation for Exponential Families of Stochastic Processes

1986 ◽  
Vol 54 (2) ◽  
pp. 191 ◽  
Author(s):  
Michael Sørensen ◽  
Michael Sorensen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Processes ◽  
Likelihood Estimation ◽  
Exponential Families

scholarly journals Maximum likelihood estimation using composite likelihoods for closed exponential families

Biometrika ◽  
2009 ◽  
Vol 96 (4) ◽  
pp. 975-982 ◽  
Author(s):  
K. V. Mardia ◽  
J. T. Kent ◽  
G. Hughes ◽  
C. C. Taylor
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Exponential Families

Maximum likelihood estimation for continuous-time stochastic processes

1976 ◽  
Vol 8 (4) ◽  
pp. 712-736 ◽  
Author(s):  
Paul David Feigin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Processes ◽  
Continuous Time ◽  
Asymptotic Theory ◽  
Likelihood Estimation ◽  
Diffusion Approximations ◽  
Limit Theory

This paper is mainly concerned with the asymptotic theory of maximum likelihood estimation for continuous-time stochastic processes. The role of martingale limit theory in this theory is developed. Some analogues of classical statistical concepts and quantities are also suggested. Various examples that illustrate parts of the theory are worked through, producing new results in some cases. The role of diffusion approximations in estimation is also explored.

scholarly journals Targeted Maximum Likelihood Estimation using Exponential Families

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Iván Díaz ◽  
Michael Rosenblum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Causal Effect ◽  
Likelihood Estimation ◽  
Parametric Models ◽  
Exponential Families ◽  
Nonparametric Model ◽  
Continuous Exposure ◽  
Targeted Maximum Likelihood Estimation ◽  
Targeted Maximum Likelihood

AbstractTargeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. The key step in any TMLE implementation is constructing a sequence of least-favorable parametric models for the parameter of interest. This has been done for a variety of parameters arising in causal inference problems, by augmenting standard regression models with a “clever-covariate.” That approach requires deriving such a covariate for each new type of problem; for some problems such a covariate does not exist. To address these issues, we give a general TMLE implementation based on exponential families. This approach does not require deriving a clever-covariate, and it can be used to implement TMLE for estimating any smooth parameter in the nonparametric model. A computational advantage is that each iteration of TMLE involves estimation of a parameter in an exponential family, which is a convex optimization problem for which software implementing reliable and computationally efficient methods exists. We illustrate the method in three estimation problems, involving the mean of an outcome missing at random, the parameter of a median regression model, and the causal effect of a continuous exposure, respectively. We conduct a simulation study comparing different choices for the parametric submodel. We find that the choice of submodel can have an important impact on the behavior of the estimator in finite samples.

Maximum likelihood estimation for continuous-time stochastic processes

1976 ◽  
Vol 8 (04) ◽  
pp. 712-736 ◽  
Author(s):  
Paul David Feigin
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Stochastic Processes ◽  
Continuous Time ◽  
Asymptotic Theory ◽  
Likelihood Estimation ◽  
Diffusion Approximations ◽  
Limit Theory

This paper is mainly concerned with the asymptotic theory of maximum likelihood estimation for continuous-time stochastic processes. The role of martingale limit theory in this theory is developed. Some analogues of classical statistical concepts and quantities are also suggested. Various examples that illustrate parts of the theory are worked through, producing new results in some cases. The role of diffusion approximations in estimation is also explored.

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