Conditional Correlation Curve: Method And Application

As an important concept in statistics,the correlation coefficient characterizes the degree of linear correlation between two variables,which is widely used in practice.However,in some practical applications,investigator are often interested in how the correlation between two variables is affected by the third variable.Therefore,based on the correlation curve,conditional correlation curve is proposed to describe the dynamic correlation between the two variables that affected by the third variable.In this thesis,the estimation of conditional correlation curve is proposed by using the approximation methods of nonparametric functions such as local polynomials and penalty splines.The consistency and asymptotic normality of the estimators are also established.Simulation studies show that the proposed method performs well in finite samples.We futher apply the proposed method to the studies of household expenditure and Saccharomyces cerevisiae cells,and conclude some intuitive statistical interpretation.