Summary: The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain and combinations of these. For inhomogeneous Poisson processes we consider Akaike's information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of ‘sample size’ needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.

This paper deals with feature selection procedures for spatial point processes intensity estimation. We consider regularized versions of estimating equations based on Campbell theorem. In particular, we consider two classical functions: the Poisson likelihood and the logistic regression likelihood. We provide general conditions on the spatial point processes and on penalty functions which ensure oracle property, consistency, and asymptotic normality under the increasing domain setting. We discuss the numerical implementation and assess finite sample properties in simulation studies. Finally, an application to tropical forestry datasets illustrates the use of the proposed method.

The aim of this study is to propose appropriate models to forecast Return on Asset (ROA) and financing of Indonesia Islamic Commercial Banks during COVID-19 pandemic. In particular, we study the models which involve reciprocal relation between ROA and financing and incorporate COVID-19 pandemic’s impact. It is crucial because the government would benefit from forecasting results to formulate the policy for the banks related to ROA and financing. We consider two models: Vector Autoregressive with exogenous variable (VARX) and spline regression, since both models are able to exploit the multivariate structure of ROA and financing and to include COVID-19 impact as predictor. The results show that the VARX outperforms spline regression in terms of RMSE. Using VARX, we deduce that ROA and financing have a positive reciprocal relationship, meaning that when ROA increases, financing would increase, and vice versa. In addition, the pandemic has significant impact on the decline of the ROA. We recommend that banks conduct an in-depth analysis to determine the appropriate form of restructuring for debtors so that it does not have a significant impact on the decrease in ROA.

Statistical inference for highly multivariate point pattern data is challenging due to complex models with large numbers of parameters. In this paper, we develop numerically stable and efficient parameter estimation and model selection algorithms for a class of multivariate log Gaussian Cox processes. The methodology is applied to a highly multivariate point pattern data set from tropical rain forest ecology.

1. 1.1. Spatial point processes are stochastic processes which model point patterns distributed in space, such as random locations of earthquake occurrences, species of trees, disease cases, and cr...