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

1995 ◽  
Vol 11 (5) ◽  
pp. 888-911 ◽  
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.

scholarly journals Numerical algorithms for constrained maximum likelihood estimation

2003 ◽  
Vol 45 (1) ◽  
pp. 91-114 ◽  
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.

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 Equilibrium Selection in Evolutionary Games with Imperfect Monitoring

2008 ◽  
Vol 45 (2) ◽  
pp. 388-402 ◽  
Author(s):  
Hsiao-Chi Chen ◽  
Yunshyong Chow
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Learning Algorithm ◽  
Large Population ◽  
Likelihood Estimation ◽  
Estimation Algorithm ◽  
Coordination Games ◽  
Imperfect Monitoring ◽  
Long Run ◽  
Two Equilibria

In this paper we analyze players' long-run behavior in evolutionary coordination games with imperfect monitoring in a large population. Players can observe signals corresponding to other players' unseen actions and use the proposed simple or maximum likelihood estimation algorithm to extract information from the signals. In the simple learning process we find conditions for the risk-dominant and the non-risk-dominant equilibria to emerge alone in the long run. Furthermore, we find that the two equilibria can coexist in the long run. In contrast, the coexistence of the two equilibria is the only limit distribution under the maximum likelihood estimation learning algorithm. We also analyze the long-run equilibria of other 2x2 symmetric games under imperfect monitoring.

A NOTE ON FERGUSSON AND PLATEN: “APPLICATION OF MAXIMUM LIKELIHOOD ESTIMATION TO STOCHASTIC SHORT RATE MODELS”

2016 ◽  
Vol 11 (04) ◽  
pp. 1650018 ◽  
Author(s):  
LUCA VINCENZO BALLESTRA ◽  
GRAZIELLA PACELLI ◽  
DAVIDE RADI
Keyword(s):  
Maximum Likelihood ◽  
Interest Rate ◽  
Maximum Likelihood Estimation ◽  
Stochastic Models ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Analytical Expression ◽  
Interesting Paper ◽  
Short Rate Models

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.

scholarly journals The Optimal Control and MLE of Parameters of a Stochastic Single-Species System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Huili Xiang ◽  
Zhijun Liu
Keyword(s):  
Optimal Control ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Likelihood Estimation ◽  
Single Species ◽  
Threshold Value ◽  
Estimation Of Parameters ◽  
Control Threshold

This paper investigates the optimal control and MLE (maximum likelihood estimation) for a single-species system subject to random perturbation. With the help of the techniques of stochastic analysis and mathematical statistics, sufficient conditions for the optimal control threshold value, the optimal control moment, and the maximum likelihood estimation of parameters are established, respectively. An example is presented to illustrate the feasibility of our theoretical results.

Sign in / Sign up

Export Citation Format

Share Document