• Information Technology
  • Human Resources
  • Careers
  • Giving
  • Library
  • Bookstore
  • Active Living
  • Continuing Education
  • Go Dinos
  • UCalgary Maps
  • UCalgary Directory
  • Academic Calendar
My UCalgary
Webmail
D2L
ARCHIBUS
IRISS
  • Faculty of Arts
  • Cumming School of Medicine
  • Faculty of Environmental Design
  • Faculty of Graduate Studies
  • Haskayne School of Business
  • Faculty of Kinesiology
  • Faculty of Law
  • Faculty of Nursing
  • Faculty of Nursing (Qatar)
  • Schulich School of Engineering
  • Faculty of Science
  • Faculty of Social Work
  • Faculty of Veterinary Medicine
  • Werklund School of Education
  • Information TechnologiesIT
  • Human ResourcesHR
  • Careers
  • Giving
  • Library
  • Bookstore
  • Active Living
  • Continuing Education
  • Go Dinos
  • UCalgary Maps
  • UCalgary Directory
  • Academic Calendar
  • Libraries and Cultural Resources
View Item 
  •   PRISM Home
  • Graduate Studies
  • The Vault: Electronic Theses and Dissertations
  • View Item
  •   PRISM Home
  • Graduate Studies
  • The Vault: Electronic Theses and Dissertations
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Some Improvement on Convergence Rates of Kernel Density Estimator

Thumbnail
View
ucalgary_2014_xie_xiaoran.pdf
Download
ucalgary_2014_xie_xiaoran.pdf (832.6Kb)
Advisor
Wu, Jingjing
Author
Xie, Xiaoran
Accessioned
2014-08-06T17:52:11Z
Available
2014-11-17T08:00:38Z
Issued
2014-08-06
Submitted
2014
Other
Kernel Density Estimation
Geometric Extrapolation
Bias Reduction
Mean Squared Error
Convergence Rate
Subject
Statistics
Type
Thesis
Metadata
Show full item record

Abstract
This M.Sc. thesis focuses on improving the convergence rates of kernel density estimators. Firstly, a bias reduced kernel density estimator is introduced and investigated. In order to reduce bias, we intuitively subtract an estimated bias term from ordinary kernel density estimator. Theoretical properties such as bias, variance and mean squared error are investigated for this estimator and comparisons with ordinary kernel density estimator and location-scale kernel density estimator are made. Compared with the ordinary density estimator, this estimator has reduced bias and mean squared error (MSE) of the order O(h^3) and O(n^(-6/7)),respectively, and even further reduced orders O(h^4) and O(n^(-8 9)) respectively when the kernel is chosen symmetric. Secondly, we propose a geometric extrapolation of the location-scale kernel estimator and a geometric extrapolation of the bias reduced kernel estimator introduced above. Similarly, we investigate their theoretical properties and compare them with the geometric extrapolation of ordinary kernel estimator. These results show that among the three geometric extrapolated kernel estimators, the one based on bias reduced kernel estimator has smallest bias and MSE. The geometric extrapolation of bias reduced kernel estimator can improve the convergence rates of bias and MSE to O(h^6) and O(n^(-12/13)) respectively for symmetric kernels. The geometric extrapolation of location-scale kernel estimator can reduce bias and MSE of location-scale kernel estimator, however it has bias and MSE with a slower rate than those of the geometric extrapolation of ordinary kernel estimator. In order to assess nite sample performances of the proposed estimators, Monte Carlo simulation studies based on small to moderately large samples are carried out. Finally, an analysis of the old faithful geyser data are presented to demonstrate the proposed methods. Both the simulation studies and the real data analysis consolidate our theoretical findings.
Corporate
University of Calgary
Faculty
Graduate Studies
Doi
http://dx.doi.org/10.5072/PRISM/27828
Uri
http://hdl.handle.net/11023/1671
Collections
  • The Vault: Electronic Theses and Dissertations

Browse

All of PRISMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

  • Email
  • SMS
  • 403.220.8895
  • Live Chat

Energize: The Campaign for Eyes High

Privacy Policy
Website feedback

University of Calgary
2500 University Drive NW
Calgary, AB T2N 1N4
CANADA

Copyright © 2017