Maximum likelihood estimation using the empirical fisher information matrix

In a very recent and interesting paper, Fergusson and Platen (2015) investigate the applicability of the maximum likelihood (ML) method for estimating the parameters of some of the most popular stochastic models for the short interest rate. One of the main results of this paper is the analytical expression of the so-called observed Fisher information matrix for the Vasicek model at the ML point. However, in such a matrix some entries are not derived correctly and one entry is left unspecified. In the following, we provide the correct analytical expression of that matrix.

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Numerical algorithms for constrained maximum likelihood estimation

The ANZIAM Journal ◽

10.1017/s1446181100013171 ◽

2003 ◽

Vol 45 (1) ◽

pp. 91-114 ◽

Cited By ~ 5

Author(s):

Z. F. Li ◽

M. R. Osborne ◽

T. Prvan

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Information Matrix ◽

Numerical Algorithms ◽

Trust Region ◽

Likelihood Estimation ◽

Quadratic Model ◽

Mixture Density ◽

Constrained Maximum Likelihood Estimation ◽

Constrained Maximum Likelihood

AbstractThis paper describes a SQP-type algorithm for solving a constrained maximum likelihood estimation problem that incorporates a number of novel features. We call it MLESOL. MLESOL maintains the use of an estimate of the Fisher information matrix to the Hessian of the negative log-likelihood but also encompasses a secant approximation S to the second-order part of the augmented Lagrangian function along with tests for when to use this information. The local quadratic model used has a form something like that of Tapia's SQP augmented scale BFGS secant method but explores the additional structure of the objective function. The step choice algorithm is based on minimising a local quadratic model subject to the linearised constraints and an elliptical trust region centred at the current approximate minimiser. This is accomplished using the Byrd and Omojokun trust region approach, together with a special module for assessing the quality of the step thus computed. The numerical performance of MLESOL is studied by means of an example involving the estimation of a mixture density.

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Generalized Truncation Positive Normal Distribution

Symmetry ◽

10.3390/sym11111361 ◽

2019 ◽

Vol 11 (11) ◽

pp. 1361

Author(s):

Héctor J. Gómez ◽

Diego I. Gallardo ◽

Osvaldo Venegas

Keyword(s):

Maximum Likelihood ◽

Normal Distribution ◽

Fisher Information ◽

Fisher Information Matrix ◽

Information Matrix ◽

Maximum Likelihood Estimators ◽

Real Data ◽

Data Sets ◽

New Model ◽

Positive Support

In this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model’s basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model’s good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption.

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A New Two-Parameter Lindley Distribution

Nepal Journal of Mathematical Sciences ◽

10.3126/njmathsci.v1i0.34157 ◽

2020 ◽

Vol 1 ◽

pp. 33-42

Author(s):

Rama Shanker ◽

Umme Habibah Rahman

Keyword(s):

Maximum Likelihood ◽

Goodness Of Fit ◽

Fisher Information Matrix ◽

Information Matrix ◽

Likelihood Estimation ◽

Lifetime Data ◽

Lindley Distribution ◽

Method Of Maximum Likelihood ◽

Two Parameter ◽

Family Of Distributions

In this paper, a new two-parameter Lindley distribution has been proposed. Descriptive statistical properties along with order statistics, Fisher information matrix and confidence interval of the proposed distribution have been discussed. Parameters are estimated by the method of Maximum Likelihood estimation. A real lifetime data has been presented to test the goodness of fit of the proposed distribution over other one parameter and two –parameter Lindley family of distributions.

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Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems

Econometric Theory ◽

10.1017/s0266466600009919 ◽

1995 ◽

Vol 11 (5) ◽

pp. 888-911 ◽

Cited By ~ 26

Author(s):

Pentti Saikkonen

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Asymptotic Theory ◽

Information Matrix ◽

Sufficient Conditions ◽

Likelihood Estimation ◽

Parameter Estimator ◽

Long Run ◽

Simple Regression Model ◽

Stochastic Equicontinuity

Problems with the asymptotic theory of nonlinear maximum likelihood estimation in integrated and cointegrated systems are discussed in this paper. One problem is that standard proofs of consistency generally do not apply; another one is that, even if the consistency has been established, it can be difficult to deduce the limiting distribution of a maximum likelihood estimator from a conventional Taylor series expansion of the score vector. It is argued in this paper that the latter difficulty can generally be resolved if, in addition to consistency, an appropriate result of the order of consistency of the long-run parameter estimator of the model is available and the standardized sample information matrix satisfies a suitable extension of previous stochastic equicontinuity conditions. To make this idea applicable in particular cases, extensions of the author's recent stochastic equicontinuity results, relevant for many integrated and cointegrated systems with nonlinearities in parameters, are provided. As an illustration, a simple regression model with integrated and stationary regressors and nonlinearities in parameters is considered. In this model, the consistency and order of consistency of the long-run parameter estimator are obtained by employing extensions of well-known sufficient conditions for consistency. These conditions are applicable quite generally, and their verification in the special case of this paper suggests how to proceed in more complex models.

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FISHER INFORMATION MATRIX FOR CROVELLI'S AND GAMMA BETA II BIVARIATE DISTRIBUTIONS

REVISTA BRASILEIRA DE BIOMETRIA ◽

10.28951/rbb.v39i2.476 ◽

2021 ◽

Vol 39 (2) ◽

pp. 350-361

Author(s):

Ana Paula Coelho Madeira SILVA ◽

Adélia Conceição DINIZ

Keyword(s):

Maximum Likelihood ◽

Nonlinear Equations ◽

Fisher Information ◽

Beta Distribution ◽

Fisher Information Matrix ◽

Information Matrix ◽

Maximum Likelihood Estimators ◽

System Of Nonlinear Equations ◽

Bivariate Gamma Distribution ◽

The City

In this paper, a system of nonlinear equations for the maximum likelihood estimators as wel as the exact forms of the Fisher information matrix for Crovelli's bivariate gamma distribution and bivariate gamma beta distribution of the second kind are determined. An application of the results to the rainfall data from the city of Passo Fundo are provided.

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