Serial Correlation Test Of Trace Regression And Its Application

With the continuous development of the digital era,data is becoming more and more important in life.In the past,our understanding of data was limited to the narrow sense of the phenomenon itself or the value obtained through observation,measurement and calculation.In general,we call it numerical data.With the advent of the era of big data,data in real life is no longer limited to the previous single numerical data,the scope of data definition is not as small as before,the definition of data is more and more broad,its form is more and more diversified,which makes our way of data processing should be updated with different forms of data.Trace Regression model,which has emerged in recent years,is a good example for processing covariate matrices.Compared with other regression models,the covariate of trace regression model is a matrix and has attracted attention due to its good processing of correlation between rows and columns.Despite extensive research conducted by numerous scholars on the theory and applications of trace regression models,limited attention has been given to the investigation of residual sequence autocorrelation tests in this particular model.Based on this,this thesis proposes to use the empirical likelihood method to construct a test statistic to test the serial correlation problem of the residual term of the Trace Regression model.In this thesis,we focus on high-dimensional matrix data.Considering the low-rank structure exhibited by the parameter matrix,this study employs the least squares estimation method with a nuclear norm penalty to estimate the parameters.Through theoretical proof,we verify that the constructed statistics obey the asymptotic chi-square distribution.The numerical simulation results also prove the validity of the constructed test statistics.In the empirical analysis part,this thesis uses the global fire point data in the field of environmental protection as the actual data to discuss the series correlation problems of trace regression model,which provides a theoretical basis for further research and analysis.All parts of this thesis is divided into five parts,which are arranged as follows:Part Ⅰ: Introduction.This part expounds the background and significance of topic,summarizes and comments on the literature based on the existing research at home and abroad,and puts forward the idea and basic framework of this thesis,explains the innovation point and research significance of this thesis,and concludes the areas that need to be further improved in the research process.Part Ⅱ: Related theoretical basis.This part expounds the theoretical basis of matrix data,trace regression model and serial correlation test respectively,and leads to the problem of testing the correlation of the serial items of the residual trace regression model,which provides the theoretical basis for the serial correlation test and empirical research in the following section.Part Ⅲ: Serial correlation test of trace regression model.This part is the core part of the whole thesis.It mainly introduces how to construct test statistics and the corresponding test method,the progressive distribution of test statistics and the proof of theorem and result.It verifies the feasibility of the method through stochastic numerical simulation.Part Ⅳ: Empirical analysis.Focusing on the field of environmental protection,the fire data from satellite remote sensing monitoring is used for actual data analysis,mainly domestic fire data,supplemented by foreign fire data for further verification,so as to illustrate the feasibility of the theory and method in practical life.Part Ⅴ: Conclusion and prospect.The results in each chapter are summarized to illustrate the conclusions obtained in this thesis,and the unsolved problems and future research directions are prospected.