﻿ 似乎不相关模型在粮食产量研究中的应用 Application of Seemingly Unrelated Model in the Study of Food Production

Vol.06 No.04(2017), Article ID:21290,6 pages
10.12677/AAM.2017.64057

Application of Seemingly Unrelated Model in the Study of Food Production

Bo Wang*, He Zhang

School of Math and Physics, China University of Geosciences, Wuhan Hubei

Received: Jun. 18th, 2017; accepted: Jul. 4th, 2017; published: Jul. 7th, 2017

ABSTRACT

The traditional linear model is usually used in the study of grain yield ,in which the error terms are assumed independent of each other, and the parameters are estimated by the least squares method. In order to improve the estimation accuracy, seemingly unrelated model is introduced. Least squares model and seemingly unrelated model were built with the data that the yield, planting area and irrigation area of rice, wheat and corn between 1990 and 2009. The result showed that parameter variance of seemingly unrelated model is smaller than the least square model. The output of the three kinds of grain between 2010 and 2015 was predicted by the two models, and the average prediction error of seemingly unrelated model was smaller. It shows that there is some correlation between the yields of the three grain crops, and the seemingly unrelated model is better than the traditional least square model.

Keywords:Seemingly Unrelated, Least Square Method, Grain Yield, Parameter Estimation

1. 引言

2. 模型理论

2.1. 最小二乘模型理论

(1)

(2)

(2)式是常见的多元线性模型，也叫线性回归模型 [2] 。对参数的估计，常采用最小二乘法，当矩阵列满秩时，的最小二乘估计量为

(3)

2.2. 最小二乘模型理论

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

3. 实例分析

3.1. 粮食产量的线性模型

(12)

(13)

(14)

3.2. 结果对比与预测

4. 总结

Table 1. Variance of the parameters of the two models

Table 2. Prediction results of the two models (Unit: Million tons)

Application of Seemingly Unrelated Model in the Study of Food Production[J]. 应用数学进展, 2017, 06(04): 481-486. http://dx.doi.org/10.12677/AAM.2017.64057

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9. NOTES

*通讯作者。