Statistical Inference In Tensor Parameter Regression Model And Its Algorithm Implementation

In recent years,tensors have gone from physics to all walks of life in our lives,and have been widely studied in traffic safety,medical diagnostics,satellite monitoring,etc.The study of tensors in linear regression models is conducive to more accurate predict the results,thereby benefiting from physical health and convenience of life.This paper studies the parameter estimation and hypothesis testing problems of tensor in general linear regression model and generalized linear regression model.For the tensor linear regression model,firstly,the point estimator of the parameter is obtained based on the least squares,and the consistency is proved.Then the approximative algorithm of the estimation is given by the CP(CANDECOMP/PARAFAC)decomposition structure of the coefficient tensor–alternating least-square;secondly,the quasi-likelihood ratio test statistic of parameter linear hypothesis test is established,and its large sample property is proved.The Mote Carlo simulation results show that the alternating least-square estimation performs well and the quasilikelihood ratio test is no significant difference between the empirical distribution of the statistics and the theoretical distribution.Finally,the method is applied to the English alphabet counting problem in text data analysis,and the more accurate prediction results are obtained.For the tensor generalized linear regression model,based on the CP decomposition of the tensor,combined with the maximum likelihood estimation method to prove the consistency of the point estimators,and further we derive the limit distribution on the test statistics.