The improved artificial bee colony algorithm for mixed additive and multiplicative random error model and the bootstrap method for its precision estimation

To solve the complex weight matrix derivative problem when using the weighted least squares method to estimate the parameters of the mixed additive and multiplicative random error model(MAM error model), we use an improved artificial bee colony algorithm without derivative and the bootstrap method to estimate the parameters and evaluate the accuracy of MAM error model. The improved artificial bee colony algorithm can update individuals in multiple dimensions and improve the cooperation ability between individuals by constructing a new search equation based on the idea of quasi-affine transformation. The experimental results show that based on the weighted least squares criterion, the algorithm can get the results consistent with the weighted least squares method without multiple formula derivation. The parameter estimation and accuracy evaluation method based on the bootstrap method can get better parameter estimation and more reasonable accuracy information than existing methods,which provides a new idea for the theory of parameter estimation and accuracy evaluation of the MAM error model.