محمود افشاری

Wavelet is one of the relatively new achievements in mathematics and has many usages in communication, engineering and medical sciences. Wavelet adapts itself with complex situations especially when densities have sudden changes. The estimation of regression function is one of the most important topics in statistics and due to excellent properties of wavelet, in this thesis used the role of wavelet to estimate regression function. In this thesis , chapter one express the definitions and terms of linear algebra , chapter two express a discussion of wavelets issues and chapter three investigates the methods of density estimation and regression by wavelet. Chapter four verifies the usage of Boundary Wavelet in estimation of regression function with a sharp changing point.