Statistica Sinica 26 (2016), 861-879 doi:http://dx.doi.org/10.5705/ss.2014.150
Abstract: For models used to describe spatial-temporal marked point processes with covariates, the high number of parameters typically involved can make model evaluation, construction, and estimation using maximum likelihood quite difficult. A further complication is that some relevant covariates may be missing from the fitted model, and the impact of these missing variables is typically unclear. Conditions are explored here under which parameters governing a space-time marked point process may be estimated simply and consistently by maximizing a partial likelihood, essentially ignoring other terms in the model and any missing covariates. Under the given conditions, the resulting estimates may have the desirable properties of maximum likelihood estimates for the full model. An application to southern California earthquake forecasting using weather data is provided.
Key words and phrases: Conditional intensity, consistency, maximum likelihood estimation, Poisson process, spatial-temporal point process, weighted least squares estimation.