Optimal Prediction In Finite Population Based On Fuzzy Points Data

In classical regression analysis, all sample data are treated uniformly in the construction of prediction model. However, in many practical applications, the effects of sample data are different. It is often that some sample data may be more important than others. So we need these data, which are important to the population, making more contributions to the fitting curve. In this paper, we give a fuzzy confidence weight to each sample data and construct a linear prediction model in finite populations based on fuzzy points data. The best linear unbiased predictor, simple projection predictor and generalized shrunken least squares predictor, which are based on fuzzy points data for the new model, are mainly investigated in our paper. Meanwhile, their statistical characteristics, which are similar to the properties of the classical linear predictor, are also discussed. The method which is proposed by us, equals to the classical linear prediction method when all the preset fuzzy weights degenerate to 1.This paper includes 6 chapters. In chapter 1, the background knowledge of linear prediction method and some existed theories are introduced . Some preparatory knowledge of fuzzy points data, Hadamard product and generalized inverse are discussed in chapter 2. In chapter 3 ,the best linear unbiased predictor (BLUP) based on fuzzy points data is obtained and its admissibility is discussed. And the conditional optimal prediction based on fuzzy points data under the situation of linear equality constraint is also investigated. Then, in chapter 4, the necessary and sufficient conditions for optimality of the SPP based on fuzzy points data are obtained and its robustness on the covariance matrix is investigated. After that, the generalized shrunken least squares predictor (GSLSP) based on fuzzy points data is presented and the necessary and sufficient conditions for superiority of GSLSP over BLUP is obtained in chapter 5. Finally, we apply our new method to an actual example, for improving its precision of prediction in chapter 6.