Statistical Inference Research Based On Vine-Copula For High Dimensional Counting Data

Counting data is widely used in many fields of biomedicine,genetics,financial insurance,clinical diagnosis,and risk control.For the study of counting data,the most common is to use the Poisson model or the negative binomial distribution model for regression analysis.With the development of science and technology and the deepening of research,the counting data of the research often has high-dimensional and nonlinear conditions.The commonly used regression models can not meet the needs of data research.Therefore,it is necessary to establish a dynamic A nonlinear model is used to describe this dynamic correlation between variables.Copula function,as a tool for correlation analysis and multivariate statistical analysis,has significant advantages in dealing with nonlinear and asymmetrical data.The microbial community data of different parts of the human body in the center is the research object,and the statistical inference procedure based on the above-mentioned data complete high-dimensional Copula model is established.In general,the work of this article can be roughly divided into the following two aspects:(1)A high-dimensional Copula model based on D-vine is established for high-dimensional count data.The Poisson distribution is used as marginal distribution and parameter estimation.The marginal distribution is jointly modeled,and the probability mass function law of the model is combined with D-vine.Decomposition,the algorithm to compute the likelihood of D-vine is used to estimate the parameters of Copula,and the microbial data sets of different parts of the human body are used for case analysis to further illustrate the validity of the model.In addition,the modeling method of this paper is also used.Compared with the traditional multivariate Copula model,the results show that the modeling method can better fit the data.(2)Based on the work of the first part,the model selection problem is studied,including the selection of the model truncation level and the selection of the simplified level.Specifically,for the truncation model,the Copula pair after each truncation level is set.For the independent Copula,the AIC values of different modelsare obtained,and the optimal truncation model and the corresponding truncation level are obtained.For the simplified model,the Copula pair after each simplified level is set as Gauss Copula,and the Vuong test is performed to obtain the most Excellent simplified model and corresponding simplified level.Compared with the traditional Copula modeling method,the proposed method has a highly flexible dependency structure,which can reduce the computational complexity of the estimation process and efficiently obtain the correlation between variables.The research in this paper adapts to the needs of practical problems for data analysis.There are some innovations in the research content,and the statistical inference method is also more distinctive,which is a valuable exploration.