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The estimation of a random design or a wave that has errors and disturbances is of particular importance in statistics and can be done in many ways.One of the methods for estimating the use of wavelets.A wavelet is a strong mathematical tool with high flexibility, which is constructed based on orthogonal bases.Considering independence or correlation between errors,The same and different time intervals examined There has been a lot of research on the correlations or uncoordinated observations. First, after briefly describing the space of functions, wavelet transforms and threshold wavelet, we will review the design of random experiments.In the following, we will describe the nonparametric estimation of the randomized design by the method of threshold wavelet in the form of multiplicity and theorem. In the end, we will examine the theory in practice by simulation and compare the optimal estimator with error types based on the mean squared error.