Non parametric density estimation via regularization

  • Author / Creator
    Lin, Mu
  • The thesis aims at showing some important methods, theories and applications about non-parametric density estimation via regularization in univariate setting. It gives a brief introduction to non-parametric density estimation, and discuss several well-known methods, for example, histogram and kernel methods. Regularized methods with penalization and shape constraints are the focus of the thesis. Maximum entropy density estimation is introduced and the relationship between taut string and maximum entropy density estimation is explored. Furthermore, the dual and primal theories are discussed and some theoretical proofs corresponding to quasi-concave density estimation are presented. Different the numerical methods of non-parametric density estimation with regularization are classified and compared. Finally, a real data experiment will also be discussed in the last part of the thesis.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Mizera, Ivan (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Karunamuni, Rohana (Department of Mathematical and Statistical Sciences)
    • Leuangthong, Oy (Department of Civil and Environmental Engineering)
    • Li, Pengfei (Department of Mathematical and Statistical Sciences)