The parameter estimation and hypothesis testing problem in the tensor linear regression model are studied. 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 quasi-likelihood 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.

tensor linear regression model; alternating least-square; quasi-likelihood ratio; CP decomposition