【作者】 李艳萍；

【导师】 施久玉；

【作者基本信息】 哈尔滨工程大学 ， 经济数学， 2009， 硕士

【摘要】 偏最小二乘回归(PLS)是构造回归方程的一种较新的多元统计方法,最早由化学界的S.Wold在1983年提出,后来日益受到统计界的关注。许多统计学家都对这种方法进行了研究。这种方法不但适用于单变量的回归分析,而且可以用于多元变量回归分析。PLS具备主成分分析、典型相关分析和OLS回归三者的某些特点,是对样本数据进行建模的一种稳健统计分析方法。本文在总结多元线性回归模型基础上,进一步认识到其存在的多重共线性问题，提出用偏最小二乘回归模型定义；从多元线性回归、主成分分析以及典型相关分析相结合三个层面上提出了偏最小二乘回归模型。对于加法模型,在各维自变量独立的情况下,使用基于基函数变换的偏最小二乘非线性回归方法得到整体模型后,可以从中提取各维自变量独立的回归关系式，分别绘出各维自变量对因变量的函数曲线,进一步分析它们之间的关系。从理论和实际应用方面证明了偏最小二乘回归模型的科学合理性；在论文最后一章中运用偏最小二乘回归方法分析了我国R&D分类投入与经济增长之间的关系,研究表明了中国R&D分类投入每一项都对经济增长产生一定贡献力：应用研究R&D支出对经济增长贡献率较高,表明其对我国经济增长的促进作用较为显著；基础研究R&D支出增长率对经济贡献率最高,表明其增长越快我国经济增长越猛。另外,通过实例分析验证了非线性偏最小二乘回归在经济系统中的应用的可行性。更多还原

【Abstract】 Partial Least-Squares is a new multivariate analysis method to build the equation about regression, which was fist proposed by economist S.Wold in 1983.Partial Least-Squares Regression was increasingly concerned later. Many statisticians study this method. The method is not only used for single variable regression analysis, but also multiple analyses. PLS with principal component analysis, canonical correlation analysis and OLS regression of certain characteristics of the three is a sample data model of a robust statistical analysis.This paper is based on summarizing the multivariate linear regression model, further to recognize the existence of multi-collinearity problems, giving the partial least-squares regression model to definite; from the combinations of multiple linear regression, principal component analysis and canonical correlation analysis to propose the partial least squares regression model. For additive models, in that the independent variables, the use of transform basis function based on partial least squares approach to the overall non-linear regression model can be extracted from the variable that the return of an independent relationship, respectively, all drawn from the variables on the dependent variable of the function curve, then further analyze the relationship between them. From the application of theoretical and practical field we prove scientific rationality of partial least-squares regression model; in the last chapter, by using the partial least-squares regression we analysis the relationship between our R & D classification of the input and economic growth, our research shows that each the classified input of China R & D bring about a specific contribution to economic growth; the expenditures of applying the research on R & D produces a supreme contribution rates to economic growth, and our results indicate that it produces promote more significant promoted effects in Chinese economic growth; the expenditure growth rate of basic research R & D produces a supreme contribution rates to economic, which shows that the more it increase quickly the more our national economic has grown quickly. In addition, by researching the case we verified the non-linear partial least-squares regression in the economic system feasibility.更多还原