Semiparametric Generalized Linear Models with the gldrm Package.

Area of Science:

• Statistics
• Computational Statistics
• Statistical Modeling

Background:

• Generalized linear models (GLM) traditionally rely on specific parametric distributions (e.g., Poisson).
• A recently proposed semiparametric GLM extends this by assuming a more general exponential tilt family for the response.
• Estimating parameters in such semiparametric models requires specialized algorithms.

Purpose of the Study:

• To introduce a novel algorithm for estimating and performing inferences within the semiparametric generalized linear model framework.
• To enhance computational stability and efficiency compared to existing algorithms.
• To provide a practical implementation of the algorithm for broader use.

Main Methods:

• The study develops an algorithm to estimate regression coefficients and the unspecified reference distribution by maximizing a semiparametric likelihood.
• The algorithm incorporates computational improvements for stability and efficiency.
• The method is designed to handle both small and large support for the nonparametric response distribution.

Main Results:

• The new algorithm demonstrates improved computational stability and efficiency for semiparametric GLM inference.
• It performs effectively across a range of support sizes for the nonparametric response distribution.
• The algorithm is successfully implemented in the R package 'gldrm'.

Conclusions:

• The developed algorithm provides a robust and efficient tool for semiparametric GLM.
• The 'gldrm' R package facilitates the application of these advanced statistical models.
• This work advances the practical application of flexible statistical modeling techniques.