| The evaluation is the most important foundation of the measurement and metric in Social Economics. Some people even call our time is an evaluation ages. Numerous evaluation models all refer to collection of indexes. The collection indexes of previous evaluation methods were almost appointed beforehand artificially, however, it is the mainly trend that the indexes are computed scientifically from samples, for that to construct a more scientific evaluation model is very required. The paper studies an evaluation model which was introduced in the literature [1] accepted by SCI. The model belongs to a generalized linear regression model with convex constraint, that the regression coefficients and dependent variables are all unknown but they are both satisfied some convex constraint conditions. This paper is to deeply study the theory and algorithm of this model.The author discusses the problems from the foliowings:(1) Further studies of the LSE algorithm of the evaluation model with the alternating projection method between two sets are present. The existence of the LSE roots is proved. The author also presents the ridge estimate of the parameters by alternating projection when the designing matrix is multicollinearity.(2) Using the EM algorithm, the author deduced the detail process of MLE method of the evaluation model and improved the integral solution method in the EM algorithm. This makes the program design convenient, and the author compiled a special program for this algorithm. Numerical experiment shows that the algorithm is better.(3) The author discusses the MLE method of the evaluation model and its convergence and asymptotic property. Firstly, we present the definition of the convergence of EM algorithm and the convergence of the series generated by the EM algorithm. Then we detailed proved the EM algorithm is convergent and the series generated by the EM algorithm is also convergent. Secondly, we discussed the asymptotic property of the EM algorithm. When the evaluation expert tend to infinite, we obtained the limited form of the EM algorithm. By the asymptotic normality of MLE, the limited form solution of the EM algorithm is convergent in probability to its real value. We also proved that the series of EM algorithm is convergent in probability to the optimal solution of the limited form. So the MLE of parameters of the evaluation model based on the EM algorithm is convergent in probability to the parameters' real value. We perfectly complete the asymptotic theory of the MLE of the evaluation model.(4) A difficult problem in the total factor productivity (TFP) computation was solved by applying our evaluation model. The number of regression coefficients is more than the samples, which is the most computing difficulty in TFP computation solved by the production function. Professor Tinbergen, who is a gainer of the Novel prize, greatly reduced the number of regression coefficients by assuming that the regression coefficients have a form of exponential functions. But this assumption is more strictly and not in accord with the practice. If we assumed that the TFP is a constant value within a short time interval in the production function, that is said that the coefficients are segment indeterminate, we can apply our evaluation model to solve it. This assumption is obviously feasible and reasonable.Comparing with the framework of generalized linear regression model, factor analysis model and path analysis model, we can find that our evaluation model have more theoretical significance in consummating the model structure of linear regression.Deeply comprehending the LSE algorithm of the evaluation model with the alternating projection method between two sets and the MLE of this model with the EM algorithm, we can find the technique of the algorithm structure.Because of the importance of the TFP measurement, we can find that our model and algorithm have an important application value and practice significance.
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