Wavelet estimation method has always been one hot and difficult problem in Statistics, and has wide application value in data compression, turbulence analysis, image and signal processing and seismic exploration, etc. The research object of this paper is the application of wavelet estimation method in mathematical statistics, focuses on the basic theory of wavelet estimation method, the types of threshold, and research achievements of the wavelet estimation method under complete data, incomplete data and longitudinal data. Due to the complexity and incompleteness of the data, traditional research methods are no longer applicable. It needs to combine with the characteristics of left truncated data, right censored data, missing data and longitudinal data, use the plug-in, calibration regression, imputation and inverse probability weighting methods. The nonlinear wavelet estimators of estimated functions are constructed, study the asymptotic expansion for mean integral square error (MISE) of nonlinear wavelet estimators and prove the asymptotic normality of estimators. The asymptotic expansions of MISE are still true for the estimated function with finite discontinuous points, and verify the uniform convergence rate of nonlinear wavelet estimators in Besov spaces, which contain unsmoothed functions; as well the wavelet method is used to study the consistency and convergence rate of the parametric and nonparametric parts for the semi-parametric regression models. Finally, the potential development direction of wavelet method is briefly discussed.