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Statistics 526 Term 2 2005-6
Smoothing Methods/Functional Data Analysis
Running Outline and Course Notes
The following is based on 2 lectures per week, each lecture being
1 hour and 20 minutes. We probably have about 13 weeks or 25 lectures
(with holidays).
PROJECTS
ADDITIONAL??:
Green's functions?? differential equations?? differential operators??
Estimating derivatives - there is little here - put some with locpoly?
Lecture 20: Registration
Lectures 18-19: FDA Regression
some other fda, for fun
Lecture 17: more FDA PCA:
lecture notes and
R code.
R code ||
choosing lambda
||
Here is some sketchy
theory - I probably won't
cover this, it's for your info.
another pca method
Lecture 16: FDA: intro to PCA
Homework 3 due, using
mouse data file||
lecture notes and
R code:
grades.pc.txt,
weather.pc.txt,
ellipse.txt,
mouse.pc.txt,
fda.pc.txt
explanation of Rholf and Archie basis method
with some R code.
Lectures 14 and 15: FDA pointwise analysis etc
lecture notes (this was
previously posted under Fri Mar 24)
R code:
R_read_in_wheel.txt
for reading in data and omitting problem points;
R_fda_mean_explore.txt
for finding point-wise means, SD's and SE's;
R_fda.mean_LS.txt
using least squares with a flexible basis;
R_leave_1_curve_out.txt
for cross-validation;
R_fda_sim.txt
for simulating Gaussian processes, for a small simulation study of CV
Using fda library in R with
lecture notes
and
R example.
Documentation for R's fda library - big pdf file. You should
also download the pdf file at the R-cran site.
Lecture 13: Using linear mixed effects models
Lectures 10, 11 and 12: Smoothing splines/P-splines/L-splines
and penalized likelihood methods
lecture notes||
R code CORRECTED - some
errors with predict.smooth.Pspline syntax
||
1998-99 notes ||
Reproducing
Kernel Hilbert Spaces Made Easy, for those who want a
very theoretical treatment of splines (not covered in class)
||
connection with Gaussian processes, machine learning, Bayesian analysis
Lecture 9 Regression splines and Bsplines:
lecture notes and
R code
Lecture 8
Hat matrix, equivalent number of parameters, eigenanalysis
of the hat matrix
lecture notes and
R code.
Homework 4: due Fri Mar 3
HW4, data file to be e-mailed.
Lecture 7:
Discuss approaches and problems with
high dimensional x's.
Analyze Vancouver pm.10 data
using a semi-parametric model.
Here are brief 1998/9 notes on
multivariate smoothing
and
generalized additive models.
Here are 2003 notes on
using gam in R/Splus.
I am not going to spend much time on gam.
Lectures 5 and 6: bandwidth choice
plug-in||
cv lecture notes||
R code for leave one point out CV||
R code for leave one curve out CV
||
Previous notes on
choice of smoothing parameter: my second generation
ROT is off a bit here. This contains plug-in, CV,
proof of shortcut formula for CV. In addition, there is
the hat matrix and the effective number of parameters (which
we WILL cover ...).
Lectures 2, 3 and 4:
Local polynomial regression, local constant regression (Nadaraya-Watson)
N-W:
lecture notes||
R code||
Homework is on pages 0-2 and 0-13 of the lecture notes.||
revised lecture notes||
more R code||
Here, in section 5, you'll find
detailed proofs
Local polynomial:
notes||
some R code||
mouse data file||
Detailed proofs are found in 1998-99 notes.
Lecture 1:
You'll tell me about your background and interest. I'll introduce
you to some basic concepts in smoothing
via examples in R - see
Methods an in-class handout
describes some smoothing methods and applies them to a fictitious data
set. I'll also show a few applications of Functional Data Analysis.
Mice wheel running:
looking at body mass and growth rates
Mosquito wings:
Rohlf and Archie paper;
wings in polar coordinates;
pc analysis on un-aligned wings;
pc analysis on aligned wings
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