An integer-valued spatial autoregressive model with application to COVID-19 counts.

Area of Science:

• Statistics
• Spatial Statistics
• Count Data Analysis

Background:

• Integer-valued count data often exhibit spatial dependencies.
• Traditional models may not fully capture these complex spatial relationships.
• Accurate modeling is crucial for applications in epidemiology and criminology.

Purpose of the Study:

• To develop an integer-valued spatial autoregressive model using negative binomial thinning.
• To analyze the properties and estimation methods for the proposed model.
• To assess the model's performance in fitting and predicting real-world spatial count data.

Main Methods:

• Development of an integer-valued spatial autoregressive model.
• Parameter estimation using conditional least squares, weighted conditional least squares, conditional maximum likelihood, and Yule-Walker methods.
• Derivation of asymptotic properties for the estimators.

Main Results:

• The proposed model effectively captures spatial dependencies in integer-valued count data.
• Simulation studies validate the model's performance.
• The model demonstrates excellent fitting and predictive capabilities on COVID-19 and crime datasets.

Conclusions:

• The negative binomial thinning-based spatial model provides a robust framework for count data analysis.
• The model offers superior performance in capturing spatial dependencies compared to existing methods.
• The approach is applicable to various fields requiring spatial count data modeling, such as public health surveillance.