张量线性回归模型中的参数估计与假设检验问题

Parameter estimation and hypothesis testing problems in tensor linear regression model

研究张量线性回归模型中的参数估计与假设检验问题,先基于最小二乘法获得参数的点估计量,证明其相合性,并结合系数张量的CP(CANDECOMP/PARAFAC)分解结构给出该估计的近似算法--交替最小二乘法;其次建立了参数线性假设检验的拟似然比检验统计量,并证明其大样本性质。Monte Carlo模拟结果表明:交替最小二乘估计表现良好,且拟似然比检验统计量的经验分布与理论分布无显著差异,将该方法运用于文本数据分析中的英文字母计数问题,获得比较准确的预测结果。

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.