The Parameter Estimation Of Sginar(s) Models With Missing Data

Missing data can lead to serious problems,including reduced sample size,estimation bias,algorithmic problems,reducing the efficiency of time series analysis methods,and affecting the accuracy and validity of results.Therefore,proper handling of missing data is an important part of data analysis in statistics.Therefore,this paper studies the parameter estimation problem of the SGINAR(s)models with missing data.In this paper,the applicability of several methods for processing missing data is studied for the SGINAR(s)model with missing data.The method of selecting the initial value of parameters in the iterative process of Li estimation method and Bridge estimation method in the imputation method is given:based on the parameter estimation obtained by the direct deletion method as the initial value of the iteration,we name the imputation method based on the direct deletion method to select the initial value of the iteration as I-Li estimation method and I-Bridge estimation method.First,the amplitude modulation functionδ_i is introduced,andδ_iX_i is used instead ofX_i in the complete data in the direct deletion method,and the moment estimation and asymptotic properties of the parameters are obtained,and the random simulation shows that this method of initial value selection has good applicability.In the single-value imputation method,the observed sample mean is used to replace the missingX_i in the data,and the amplitude modulation functionδ_i is also introduced to give the moment estimation of the parameters,and the stochastic simulation results show that the imputation method is slightly better than the direct deletion method when the deletion rate is high.Second,under the completely random deletion mechanism,the parameter estimation problem of SGINAR(s)models with different values of s was studied by direct deletion method,I-Li estimation method and I-Bridge estimation method.The SGINAR(1)model degenerates into the NGINAR(1)model when s=1,and the SGINAR(s)models when s≥2 has a wider range of applications.The deletion method and the imputation method were applied to solve the problem of missing data in the SGINAR(s)models,and the applicability of the direct deletion method,I-Li estimation method and I-Bridge estimation method was obtained according to the basic principles of the two types of methods and the definition and nature of the model.The feasibility of the three methods for processing missing data in the SGINAR(s)models was verified by stochastic simulation,and the superiority of the direct deletion method,I-Li estimation method and I-Bridge estimation method was compared according to the simulation results.Finally,the method studied in this paper was applied to a set of seasonal tuberculosis case data,and through the analysis of the parameter estimation results,it can be seen that the estimated results are basically consistent with the actual experience.