The Statistical Inference Method Of Varying-coefficient Models Based On The Piecewise B-spline Function

Varying-coefficient models has been widely used in the information fields of bi-ology,medicine,environment and finance.In general,there are a lot of data on the problems which we study,and the coefficient function in the varying-coefficient mod-els may have jump points.The appearance of jump points means the occurrence of major events,which often affect the normal economy and life of human beings.The jump points detected accurately can help people identify opportunities and avoid risks.Spline method has a good performance not only in detecting jump points,but al-so in computational speed,stability and smoothness.Therefore,this paper proposes a method of jump detection and B-splines function estimation anout varying-coefficient models.Firstly,this paper describes the research status of varying-coefficient models in longitudinal data and independent data.Then a better method at present is reviewed,i.e.local linear kernel estimation.Because of the shortcomings in computing speed and jump detection,we introduce the method of B-spline estimation.The first esti-mator is obtained when the knot sequence is quasi-uniform.Next,adding a knot with multiplicity p+1 at the fixed point x on the support[a,b]to get the second estimator.Then,the difference of the residual of sum squares DRSS(x)between the two esti-mators can be calculated for any points x ?(a,b).Finally,the coefficient function with jumps can be fitted based on piecewise B-spline function.