Study On Jump Regression Analysis And Its Application

In many applications, random noise are contained in observed data. Particularly,conventional local smoothing procedures is not statistically consistent at jump positions of the true regression function. Therefore, it is one of the hot topics of data analysis to denoise and preserve jumps both in statistics and engineering field. Based on the theory of jump-preserving regression, this paper applied piecewise local polynomial regression method in both univariate and multivariate data analysis,which can obtain better estimation. This algorithm is achieved by form of matrix. For boundary and singular problems on observations with noise,an improved method is proposed. This paper put forward "4 quadrants jump regression according to the gradient". The inclined jump boundary and singularity are solved at the same time with the same window width. The numerical experiments and real data analysis show the superiority of our arithmetic.