Sufficient Conditions for the Consistency of Maximum Likelihood Estimation Despite Misspecification of Distribution in Multinomial Discrete Choice Models

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.

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A simultaneous decision-making approach to model the demand for freight transportation

Canadian Journal of Civil Engineering ◽

10.1139/l91-062 ◽

1991 ◽

Vol 18 (3) ◽

pp. 515-520 ◽

Cited By ~ 14

Author(s):

W. M. Abdelwahab ◽

M. A. Sargious

Keyword(s):

Maximum Likelihood ◽

Discrete Choice ◽

Choice Model ◽

Mode Choice ◽

Freight Transportation ◽

Choice Models ◽

Ordinary Least Squares ◽

Discrete Choice Models ◽

Estimation Methods ◽

Complete Model

The application of discrete choice models (e.g., logit, probit) to study modal choice in passenger transportation has had a wide acceptance in the literature. However, little success had been reported on the application of these models to study the demand for freight transportation. This is mainly because in freight transportation a model that merely attempts to explain the choice of mode without taking into consideration other related factors, such as shipment size, is only one part of a complete model. Another type of models known as inventory-based models, which takes these factors into consideration, has been developed and applied with a greater success. However, the data requirement of these inventory models has hampered their applicability, especially in situations with limited data on goods movement. This paper presents a new approach to study the demand for intercity freight transportation. The model proposed in this paper utilizes the strength of discrete choice models (e.g., probit) in explaining the process of mode choice as one part of a complete model. The complete model is presented as a joint discrete/continuous choice model for the choices of mode and shipment size. The model is practical in that it requires the same amount and quality of data that would be required to develop a standard disaggregate mode choice model, and it can be estimated using simple two-stage estimation methods which utilizes standard probit maximum likelihood and ordinary least squares estimation techniques. Key words: disaggregate, freight transportation, maximum likelihood, mode, model, probit, shipment.

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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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