arXiv subjects

Gilberto A. Paula

Publications and source records attributed to Gilberto A. Paula.

3 recordsLinked to original sources

arXiv2026

Inference and local influence diagnostics for unit-Lindley additive partially linear models

This paper introduces a novel regression framework for modeling response variables restricted to the unit interval by proposing unit-Lindley additive partially linear models (UL-APLMs). This model class combines parsimony and interpretability of one-parameter unit-Lindley distribution with the flexibility of additive partial linear structures, enabling the coexistence of linear and smooth covariate effects. Additive terms are modeled using B-spline basis under a penalized likelihood framework to ensure smoothness. Estimation is carried out by maximizing the penalized log-likelihood function. The goodness-of-fit of the models is assessed through residual analysis, whereas the robustness of the parameter estimates and the detection of influential data points are evaluated using the local influence approach, which incorporates curvature diagnostics under case-weight and response perturbation schemes. The sensitivity and penalized observed information matrices are derived explicitly for the proposed model. Simulation studies demonstrate the accuracy of the estimation procedure under various scenarios. Real data on the assessment of the psychological profile of patients with hypopituitarism illustrate the applicability of the model, highlighting the diagnostic importance.

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arXiv2026

Stable direct estimation for GPLSIAMs using P-splines with dynamically updated boundaries

Generalized partially linear single-index additive models (GPLSIAMs) have been increasingly applied across diverse areas due to their versatility in integrating functional flexibility with parametric dimension reduction while maintaining interpretability. However, the estimation presents severe computational challenges. This paper introduces a novel stable method that uses the model matrix for each single-index effect, defined by its single-index coefficients, and the penalized complete Fisher information matrix to dynamically update the boundaries of the single-index covariates within a unified iterative framework. The derived model matrices enable the fast computation of the estimated effective degrees of freedom and pointwise confidence bands for the single-index effects. The smoothing parameter updates are integrated into the iterative process via the generalized Fellner-Schall method, which recycles the derived matrix decompositions, thereby providing an efficient approximation to the global penalized optimization problem. Simulation studies with moderate sample sizes under non-Gaussian distributions confirm the empirical consistency of the estimation across multiple scenarios. Notably, the proposed approach remains stable where state-of-the-art competitive methods fail to recover true single-index coefficients and nonlinear functions, and is 80.13 times faster than the usual two-step method in the most computationally intensive scenario. The modeling advantage is illustrated through an application to Capital Bike Sharing data, where we deal with a single-index interaction effect for each year, with distinct single-index coefficients, a complex structure that makes competitive methods inapplicable. The proposed method is implemented in R, with functions available for reproducibility and transparency in comparisons.

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arXiv2011

A Poisson Mixed Model with Nonnormal Random Effect Distribution

We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are in general required for deriving the marginal models, we obtain the multivariate negative binomial model for a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis are proposed and two applications with real data are given for illustration.

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