محمود افشاری

One of the most important parts of statistics is the estimation of the model of data when the observations are recorded with an error. If the observations are not time-dependent, we will face the regression function estimation problem and if the observations are recorded over the time, then we will have a time series problem. In this thesis, in order to estimate regression function, a new Bayesian wavelet thresholding estimation based on the mixture prior distribution is considered. In the following, considering that the data are observed over the time for unit root hypothesis testing of time series a new Bayesian test is proposed. In each section, we use a simulation study in order to evaluate the performance of the proposed method in comparison with existing methods. An experimental study in the unit root hypothesis testing the Shanghai Composite Index daily return data and the daily exchange rate of the German Marc with respect to the Greek Drachma are used in time series section and the galaxy is used in the nonparametric regression.