正态云线性回归模型及其最小二乘参数估计方法  

Normal Cloud Linear Regression Model and Its Least-Squares Parameter Estimation Method

作　　者：龚艳冰 戴靓靓 刘高峰 

机构地区：[1]河海大学企业管理学院,江苏常州213022

出　　处：《统计与决策》2017年第23期5-9,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(71303074);中央高校基本科研业务费专项资金资助项目(2015B28014);江苏省自然科学基金资助项目(BK20130242)

摘　　要：云模型作为定性定量转换的双向认知计算模型,利用二阶的高斯分布方法反映定性概念的随机性和模糊性。针对自变量和因变量同时具有模糊性和随机性的数据系统中的回归分析问题,文章提出了一种基于云模型的正态云线性回归模型,是经典线性回归模型和模糊线性回归模型的一般形式。首先,将正态云多元回归模型转化成关于云包络曲线和确定度的离散传统回归模型。其次,给出正态云间的包络距离的定义,并根据正态云间的包络距离对云回归参数进行最小二乘估计和误差分析。最后,用实例说明了方法的有效性和可行性。As a bi-directional cognitive computing model of qualitative-quantitative transformation, cloud model uses the two order Gauss distribution method to reflect the randomness and fuzziness of the qualitative concepts. Aiming at the regression analysis of the data system in which independent variable and dependent variable simultaneously are fuzzy and random, this paper presents a cloud-model-based normal linear regression model which is a general form of the classical linear regression model and the fuzzy linear regression model. Firstly, the paper transforms the normal cloud model into the discrete traditional regression mod- el about the cloud envelope curve and the certainty degree. Secondly, the concept of the normal cloud envelope distance is defined, and the least-square estimation and error analysis of cloud regression parameters are given based on the cloud envelop distance. Finally, an example is given to illustrate the effectiveness and feasibility of the proposed method.

关 键 词：正态云 正态云线性回归模型 包络距离 最小二乘法 

分 类 号：C812[社会学—统计学]