Adaptive LASSO estimation for functional hidden dynamic geostatistical models.

Area of Science:

• Geostatistics
• Statistical modeling
• Functional data analysis

Background:

• Geostatistical models are crucial for analyzing spatially referenced data.
• Functional data analysis extends traditional methods to handle data with functional characteristics.
• Hidden dynamic geostatistical models incorporate temporal dynamics and unobserved states.

Purpose of the Study:

• To introduce a novel model selection algorithm for functional hidden dynamic geostatistical models (f-HDGM).
• To simultaneously select relevant spline basis functions and regressors for fixed effects in f-HDGMs.
• To automatically handle irrelevant functional coefficients or entire functions associated with non-significant regressors.

Main Methods:

• The algorithm utilizes a penalized maximum likelihood estimator (PMLE) with an adaptive LASSO penalty.
• Weights for the penalty are derived from unpenalized f-HDGM maximum likelihood estimates.
• Computational efficiency is achieved through local quadratic approximation of the log-likelihood function.

Main Results:

• Monte Carlo simulations demonstrate the algorithm's effectiveness in prediction and parameter estimation under various spatiotemporal dependencies.
• Application to air quality data with weather and land cover covariates validates the algorithm's behavior and scalability.
• Penalized estimates show prediction ability equivalent to maximum likelihood estimates.

Conclusions:

• The proposed algorithm provides a robust method for model selection in f-HDGMs.
• Employing the one-standard-error rule leads to more accurate, simpler, and interpretable models.
• The algorithm offers a computationally efficient and scalable solution for complex geostatistical modeling problems.