M8CAO Bootstrap methods for nonparametric curve estimation

Faculty of Science
Spring 2011
Extent and Intensity
2/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
Ricardo Cao (lecturer), prof. RNDr. Ivanka Horová, CSc. (deputy)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
This short course includes di¤erent bootstrap methods for inference in non- parametric curve estimation (mainly in nonparametric density and regression estimation). The problem of construction of nonparametric con…dence intervals and bands for the density and the regression function will be treated. The boot- strap method will be also used to provide bandwidth selectors in kernel density estimation. A brief list of issues to be treated follows.
Syllabus
  • 1 Introduction to nonparametric curve estima- tion
  • 1.1 Nonparametric density estimation
  • 1.2 Nonparametric regression estimation
  • 2 Bootstrap methods for density estimation
  • 2.1 Bootstrap approximation for the sampling distribution of the Parzen-Rosenblatt kernel estimator
  • 2.2 Bootstrap methods for bandwith selection
  • 3 Bootstrap methods for nonparametric regres- sion estimation as in an unconditional sense.
  • 3.1 Asymptotic distribution of the Nadaraya-Watson es- timator
  • 3.2 Plug-in approximation
  • 3.3 Wild bootstrap
  • 3.4 Smoothed bootstrap in the explanatory variable
  • 3.5 Comparison of the methods
Language of instruction
Czech
Further Comments
Study Materials
The course is taught only once.
The course is taught: in blocks.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2011/M8CAO