محمود افشاری

The theory of estimates is one of the most important issues in statistics science. The estimation of density and regression functions, as well as their derivatives in statistics science, is very much considered and can be done in a variety of ways. In this thesis, the nonparametric estimator of the density and it's derivative and derivative of the regression function are investigated using linear wavelet method based on the biased data and in the besov balls. Then the derivative of the random regression function is investigated by linear wavelet method In the end, the rates of convergence of the desired estimators is studied in the form of several theorems. The results of the theoretical literature show that the wavelet method is very useful in estimating nonparametric functions that are suddenly changed.