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One of the important branches in statistics, is regression function. Nonparametric regression function is very important, because it has limited defults . One of the estimate regression's way is wavelet. Many researchers have been working and survey about this way, but more of the resurches have been defaults, for example light-tailed errors were (e.g. gaussian distribution ) and design points were distributed regularly. With removing the restrictions, we have a new perspective of wavelet's ways that show us that we can use them more efficiently. In this thesis wavelet estimation of a regression function by reducing these restrictions is survived.