Study about intensity estimation for inhomogeneous spatial point processes has become one of the main interests in recent decades. When the intensity is a function of many variables, covariates selection becomes inevitable. There have been a few works on variable selection for modelling the intensity of inhomogeneous spatial point processes. Although, in application, many penalty functions have been employed to regularization methods on spatial point processes models, the theoretical study is still restricted to a very specific penalty function. We consider the selection and estimation of regression parameter by regularized weighted and unweighted Poisson log-likelihood estimation, employing both convex and non-convex penalty functions. We provide general conditions on the penalty function to ensure the asymptotic properties of the estimates in terms of consistency, sparsity, and normality distribution.

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