Nonparametric Kernel Density Estimation
Tine Buch-Kromann
tbl@codan.dk
Contents
UNDERVISNING MANDAG ER FLYTTET TIL KL. 11.15-13 I A106.
Muligvis bliver vi nødt til at holde undervisning mandag den 19. marts kl. 8.15-10. I får
nærmere besked senere.
AFLEVERING AF EKSAMENSPROJEKT:
Deadline for aflevering af projektet er den 10. april og skal ske til Mette B. Jensen på 3. sal.
Lectures
- Monday: 11:15-13:00, HCØ - A106.
- Wednesday: 10:15-13:00, HCØ - aud. 5.
Lectures on Monday March 12 (week 6) are canceled.
Plan of the course
Literature
- W. Härdle, M. Müller, S. Sperlich, A. Werwatz, Nonparametric and Semiparametric Models, An Introduction, Springer Verlag 2004.
- J. Fan, I. Gijbels, Local Polynomial Modelling and Its Applications, Chapman & Hall, 1996.
- B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman & Hall, 1986.
- T. Buch-Larsen, J.P. Nielsen, M. Guillén and C. Bolancé, "Kernel Density Estimation for
heavy-tailed Distributions using the Champernowne trasnformation", Statistics,
39, pp. 503-518.
- M.C. Jones, "Simple boundary correction for kernel density estimation", Statistics and Computing, 3, 1993, p. 135-146.
- S.X. Chen, "Beta kernel estimators for density functions", Computational Statistics & Data Analysis, 31, 1999, p. 131-145.
Week 1: Monday, February 5
Canceled
Week 1: Wednesday, February 7
- Introduction, p.1-9, (cursory).(tex-version)
Overview of the theory and the ideas in the course.
- Histogram, p. 21-38.
This chapter goes through the construction of the histogram, claculations of the bias, variance, MSE and
MISE of the histogram, how to choose the binwidth, and the extension of the histogram, called the averaged
shifted histogram, which motivates the kernel density estimator.
- Nonparametric Density Estimation (one dimension), p. 39-53.
This chapter cencerns the kernel density estimator. We go through the derivation of the kernel density estimator,
introduce different kernel functions and look at their influence of the estimator. Moreover, we see the importance
of the bandwidth and introduce some bandwidth selection methods. We also mention confidence intervals.
Week 2: Monday, February 12
Week 2: Wednesday, February 14
- Nonparametric Density Estimation (one dimension), p. 39-66.
- Buch-Larsen, et. al. (2005): paper, slides, thesis.
- Questions to the project.
Week 3: Monday, February 19
Week 3: Wednesday, February 21
Week 4: Monday, February 26
Week 4: Wednesday, February 28
- Kernel Regression, p. 85-134.
- Fan and Gijbels 1996, p. 66-68, 109-113, 149-151 (choice of bandwidth in Kernel Regression)
- Silvermann 1986, p. 66-70, (bias reduction technique, higher-order kernels)
- Questions to the project.
Week 5: Monday, March 5
- Silvermann 1986, p. 66-70, (bias reduction technique, higher-order kernels)
- Jones (1993)
Week 5: Wednesday, March 7
- Jones (1993)
- Chen (1999)
- Questions to the project.
Week 6: Monday, March 12
Canceled
Week 6: Wednesday, March 14
- Questions to the project.
- Repetition from last lecture.
- Introduction to Jens Perch Nielsens talk.
- Talk of Jens Perch Nielsen, (12:00-13:00).
Week 7: Monday, March 19
- Repetition and overview of the theory.
- Questions to the project.
Week 7: Wednesday, March 21
- Repetition and overview of the theory.
- Evaluation of the course.
- Questions to the project.
The project
The project will be handed out in week 2 and deadline is April 10, 2007.
The project and the data sets can be downloaded here: