Semiparametric pseudoscore for regression with multidimensional but incompletely observed regressor.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Regression analysis with incomplete observation data presents challenges for standard statistical methods.
• Maximum likelihood estimation via expectation-maximisation (EM) is efficient but sensitive to distributional assumptions of missing data.
• Existing methods struggle with robustness and high-dimensional covariates.

Purpose of the Study:

• To develop a novel robust regression estimation method for handling incompletely observed regressors.
• To reduce sensitivity to distributional specifications in missing data models.
• To improve consistency and efficiency of regression estimators.

Main Methods:

• Proposed an expectation-maximisation (EM)-type estimation using a semiparametric pseudoscore.
• Derived the conditional expectation of the score function over incompletely observed units.
• Employed nonparametric regression to construct a working index for the semiparametric pseudoscore.

Main Results:

• The proposed estimator is more than doubly robust, ensuring consistency under correct missingness pattern or appropriate working index specification.
• Achieves optimal efficiency when both the missingness pattern and working index are correctly specified.
• Demonstrated numerical performance through Monte Carlo simulations and a real-world study on HIV/Hepatitis C coinfection.

Conclusions:

• The semiparametric pseudoscore approach offers a robust and efficient alternative for regression with incomplete observation data.
• This method mitigates the sensitivity of traditional EM algorithms to distributional assumptions.
• The doubly robust nature enhances reliability in statistical inference for complex datasets.