Wavelet Density Estimation with Applications to Finance
Xiang Zhao · 2023
This thesis represents a study of the topic of wavelet density estimation.The study includes a detailed analysis of the construction of wavelet functions, the Discrete Wavelet Transform algorithm, the study of the minimax L 2 risk of a wavelet density estimator for densities from Sobolev spaces and Besov spaces, as well as some applications of the wavelet density estimation theory to realworld financial data.Our application demonstrates that a linear wavelet density estimator behaves similarly to a kernel density estimator, whereas a nonlinear wavelet density estimator with universal threshold leads to superior prediction results.