Matrix-variate generalized linear model with measurement error

Matrix-variate generalized linear model (mvGLM) has been investigated successfully under the framework of tensor generalized linear model, because matrix-form data can be regarded as a specific tensor (2-dimension). But there are few works focusing on matrix-form data with measurement error (ME), since tensor in conjunction with ME is relatively complex in structure. In this paper we introduce a mvGLM to primarily explore the influence of ME in the model with matrix-form data. We calculate the asymptotic bias based on error-prone mvGLM, and then develop bias-correction methods to tackle the affect of ME. Statistical properties for all methods are established, and the practical performance of all methods is further evaluated in analysis on synthetic and real data sets.