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Semiparametric models: a generalized self-consistency approach.

¹University of Utah, Salt Lake City, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology

|December 4, 2010

Summary

This summary is machine-generated.

A novel O(d) estimation procedure enhances semiparametric models with unlimited dimensions. This new quasi-EM (QEM) approach offers efficient numerical handling and a dual interpretation, outperforming traditional methods.

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Area of Science:

Statistics
Statistical Modeling
Computational Statistics

Background:

Semiparametric models often involve maximum likelihood problems with potentially unlimited dimensions.
Conventional estimation methods for these models typically exhibit O(d(3)) complexity, limiting their efficiency.
There is a need for more computationally efficient estimation procedures for high-dimensional semiparametric models.

Purpose of the Study:

To propose a new O(d) estimation procedure for a broad class of semiparametric models.
To introduce a numerically efficient method for handling potentially unlimited dimensions using a Nelson-Aalen-like estimator.
To explore and compare different methods for constructing surrogate objective functions within minorization-maximization algorithms.

Main Methods:

Development of a novel O(d) estimation procedure for semiparametric models.
Utilizing a Nelson-Aalen-like estimator for efficient numerical handling of high dimensions.
Demonstration of three surrogate objective function construction methods: difference of concave functions, Expectation-Maximization (EM), and a new quasi-EM (QEM) approach.

Main Results:

The proposed O(d) estimation procedure demonstrates significant efficiency gains over conventional O(d(3)) methods.
The quasi-EM (QEM) approach provides a generalized construction of surrogate objective functions, independent of missing data representation.
Simulations and real data analysis show the new approach's effectiveness and compare it favorably with existing methods.

Conclusions:

The new O(d) estimation procedure offers a computationally efficient solution for high-dimensional semiparametric models.
The quasi-EM (QEM) method presents a flexible and powerful tool for constructing surrogate objective functions in statistical estimation.
The developed methods, particularly QEM, have broad applicability in statistical modeling, including the proportional odds model.