Representations of efficient score for coarse data problems based on Neumann series expansion

Area of Science:

• Statistics
• Statistical inference

Background:

• Coarse data problems present challenges in statistical inference.
• Efficient score computation is crucial for accurate statistical modeling.

Purpose of the Study:

• To develop novel representations for the efficient score in coarse data settings.
• To provide a unified framework for existing approximation methods.

Main Methods:

• Derivation of efficient score representations using Neumann series expansion.
• Application to both ignorable and nonignorable coarse data.

Main Results:

• New representations for the efficient score applicable to ignorable and nonignorable coarse data.
• Demonstration that existing successive approximation methods are special cases.
• Development of new algorithms for computing locally efficient scores.

Conclusions:

• The Neumann series expansion offers a powerful tool for understanding and computing efficient scores in coarse data problems.
• The derived representations unify and extend existing methodologies.
• New computational algorithms are proposed for enhanced statistical analysis.