Feature Selection in Over-dispersed Binary and Count Data Models Using Penalized Optimal Estimating Functions

Generalized linear models (GLMs) remain a core class of supervised machine learning models for binary and count responses, with feature selection commonly carried out through penalized likelihood or quasi-likelihood methods. This paper develops a feature-selection framework based on penalized Optimal Estimating Functions (OEFs), which attain Godambe optimality within a class of unbiased estimating functions and incorporate higher-order moment information without requiring full likelihood specification. Ridge, LASSO, Adaptive LASSO and SCAD penalties are introduced at the regression estimating-equation level, while dispersion is estimated jointly through an unpenalized OEF. Hyperparameters are selected using cross-validated estimating-function loss with prespecified edge and stability rules. Monte Carlo simulations with 500 replications examine Beta-Binomial and Negative-Binomial regression under moderate and high overdispersion and sparse and moderately dense signals. The results do not show uniform superiority of penalization. The unpenalized OEF generally provides the strongest coefficient coverage and RMSE benchmark, whereas the penalized OEFs provide sparse feature selection with model-dependent trade-offs between sensitivity, specificity and interval calibration. Simple post-selection refitting reduces shrinkage bias in some settings but does not restore nominal coverage because selection uncertainty remains. Penalized OEF is therefore presented as a competitive alternative when sparse selection and joint mean-dispersion estimation are both required, rather than as a uniformly better estimator.