Asymptotic Properties Of Generalized Additive Partial Linear Counting Data Model

We are surrounded by a large number of every kind of high dimensional data,especially in the fields of biology,medicine,finance,and interference factors of these observed results also showed more nonlinear effect.With the rapid development of science and technology,modern society has entered the era of big data.Therefore,the analysis and processing of high-dimensional data becomes more and more complex.On the basis of the Generalized linear models(GLM),the Generalized additive partial linear models(GAPLM)increases the nonlinear factors which influence the results.GAPLM not only inherits the excellent characteristics of GLM which can handle both continuous and discrete data type,due to the increase in consideration of nonlinear factors,it can also make the estimation precision of the model greatly improve,and the application has certain guiding significance.In this paper,we study the generalized additive partial linear models of Poisson counting data,which is the GAPLM of the response variable to satisfy the Poisson distribution,and is an important generalization of GLM combined with nonparametric estimation.This model includes both the linear and nonlinear parts,the covariates dimension of the linear part tends to infinity as the sample size tends to infinity,and non linear combination fitting approximation parameter function in polynomial spline basis,can be transformed into a linear model,and solves the dimension calculation on.In this paper,we prove the asymptotic existence,consistency and asymptotic normality of the estimator of the generalized partial linear additive model for the high dimensional longitudinal count data.The corresponding results in the literature are improved.