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Estimating functions and the generalized method of moments.
Joao Jesus1, Richard E Chandler
1Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK.
Interface Focus
|December 11, 2012
Summary
This study reviews estimating functions for statistical inference, offering a flexible framework when likelihood functions are unavailable. The methods are applied to complex systems, including stochastic rainfall models, demonstrating practical utility.
Area of Science:
- Statistics
- Statistical Inference
- Complex Systems Modeling
Background:
- Estimating functions offer a general statistical inference framework, especially when likelihood functions are difficult to specify.
- This approach is valuable for analyzing complex systems where traditional methods may be challenging.
- The generalized method of moments is a notable special case within this theory.
Purpose of the Study:
- To provide an accessible review of estimating function theory for broad applications.
- To demonstrate the practical applicability of estimating functions in complex system analysis.
- To illustrate the theory using stochastic rainfall models and simulations.
Main Methods:
- Review of estimating function theory with practically verifiable assumptions.
- Detailed examination of the generalized method of moments.
- Application to inference problems in stochastic point process rainfall models.
- Use of simulations to evaluate method performance.
Main Results:
- The review provides a clear exposition of estimating function theory, with technical details in supplementary material.
- The generalized method of moments is explored in depth.
- The methods are successfully applied to rainfall modeling, showing practical utility.
- Simulations confirm the performance of the proposed inferential techniques.
Conclusions:
- Estimating functions provide a robust and flexible framework for statistical inference in complex systems.
- The theory is applicable to real-world problems, such as modeling stochastic rainfall processes.
- The generalized method of moments is a key tool within this framework, validated by simulation studies.
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