- This paper gives the first easily computed estimators of multivariate
location and dispersion that have been shown to be sqrt(n) consistent
and to have good outlier resistance.
- Robust Multivariate Location and Dispersion
rmld.pdf
-
- This preprint shows how improve low breakdown consistent regression estimators
and outlier resistant estimators that do not have theory. The resulting estimator
is the first easily computed regression estimator that has been shown
to be sqrt(n) consistent and high breakdown. The response plot
is very useful for detecting outliers.
- Response Plots for Linear Models
lm.pdf
-
- This preprint shows how to visualize several important survival regression
models in the background of the data.
- Plots for Survival Regression
sreg.pdf
-
- This paper shows that the bootstrap is not first order accurate
unless the number of bootstrap samples B is proportional to the sample size n.
For second order accuracy, need B proportional to n^2.
- The Number of Samples for Resampling Algorithms
resamp.pdf
-
- THE FOLLOWING PREPRINTS HAVE NOT YET BEEN SUBMITTED OR NEED TO BE RESUBMITTED.
-
- Response Plots for Experimental Design
rploted.pdf
-
- Plots for Binomial and Poisson Regression
gfit.pdf
-
- 1D Regression
onedreg.pdf
- Graphical Aids for Regression.
gaid.pdf
- A Simple Plot for Model Assessment
simp.pdf
-
- Applications of a Robust Dispersion Estimator
rcovm.pdf
-
- THE FOLLOWING SIX PREPRINTS HAVE BEEN CITED BY OTHER AUTHORS.
-
- This preprint provides some of the most important theory in the field of robust statistics.
The paper shows that a simple modification to the most used but inconsistent algorithms
for robust statistics results in easily computed sqrt n consistent high breakdown estimators.
But it has been broken into a paper for regression and a paper for multivariate locations and
dispersion.
-
- Olive, D.J., and Hawkins, D.M. (2008), High Breakdown Multivariate Estimators
hbrs.pdf
- Chang, J., and Olive, D.J. (2007), Resistant Dimension Reduction
resdr.pdf
- Olive, D.J., and Hawkins, D.M. (2007), Robustifying Robust Estimators, preprint
available from
www.math.siu.edu/olive/ppconc.pdf
- For location scale families, estimators based on the median and mad have optimal robustness
properties. Use He's cross checking technique to make an asymptoticaly efficient estimator.
- Olive, D.J. (2006), Robust Estimators for Transformed Location-Scale Families.
robloc.pdf
- Olive, D.J. (2005), A Simple Confidence Interval for the Median, preprint
available from
www.math.siu.edu/olive/ppmedci.pdf
- The June 2008 ROBUST STATISTICS NOTES are below.
PLEASE CITE THIS WORK IF YOU USE IT.
- Olive, D.J. (2008), Applied Robust Statistics,
preprint available from (www.math.siu.edu/olive/run.pdf).
robnotes.pdf
-
- Web page with data sets and programs to go with the course notes.
robust.html
-
-
- Here is the second draft of Olive, D.J. (2010), Multiple Linear and 1D Regression.
regbk.htm
-
- SOME STATISTICAL INFERENCE PREPRINTS, including the ONLINE TEXT
- Olive, D.J. (2010), A Course in Statistical Theory,
preprint available from (www.math.siu.edu/olive/infer.htm), are here.
infer.htm
-
- THE NEXT NINE DOCUMENTS MAY BE OF MILD INTEREST, BUT WILL PROBABLY NEVER BE PUBLISHED.
-
- Abuhassan, H. and Olive, D.J. (2008), Inference for the Pareto, Half Normal and
Related Distributions.
std.pdf
-
- (long version of) Robustifying Robust Estimators
lconc.pdf
- Comments on Breakdown
bkdn.pdf
- The Breakdown of Breakdown
bdbd.pdf
- Prediction intervals in the presence of outliers
pi.pdf
- Slides for Response Plots for Experimental Design Talk
srplot.pdf
- This 1996 result grew into a 2002 JASA discussion paper.
dense.pdf
- This 1997 result on partitioning may be of mild interest.
part.pdf
- Slides for Visualizing 1D Regression, presented at ICORS 2003.
slides.pdf
- THE FOLLOWING ARE PREPRINTS OF PUBLISHED OR ACCEPTED PAPERS.
-
- This paper shows that OLS partial F tests, originally meant for multiple linear
regression, are useful for exploratory purposes for or a much larger class of
models, including generalized linear models and single index models.
- Chang, J. and Olive, D.J. (2010), OLS for 1D Regression Models, Communications in
Statistics: Theory and Methods, to appear.
sindx.pdf
-
- Olive, D.J. and Hawkins, D.M. (2007), Behavior of Elemental Sets in Regression,
Statistics and Probability Letters, 77, 621-624.
elem.pdf
-
- This paper shows how to construct asymptotically optimal prediction intervals
for regression models of the form Y = m(x) + e. The errors need to be iid unimodal
and emphasis is on linear regression.
- Olive, D.J. (2007), Prediction Intervals for Regression Models, Computational Statistics
and Data Analysis, 51, 3115-3122.
spi.pdf
-
- This paper shows that the variable selection software originally meant
for multiple linear regression gives useful results for a much larger class of
models, including generalized linear models and single index models, if the Mallows' Cp
criterion is used. For models I with k predictors, the screen Cp(I) < 2k is much
more effective than the screen Cp(I) < k. Use response plots to show that the
final submodel is similar to the original full model.
- Olive, D.J. and Hawkins, D.M. (2005), Variable Selection for 1D Regression Models,
Technometrics, 47, 43-50.
varsel.pdf
-
- Olive, D.J. (2005), Two Simple Resistant Regression Estimators, Computational Statistics
and Data Analysis, 49, 809-819.
mba.pdf
-
- The MBA estimator is not as good as the FCH estimator in "High Breakdown Robust
Estimators," but was the first easily computed estimator of multivariate
location and dipsersion shown (in 2004) to be sqrt(n) consistent and outlier resistant
The median ball estimator is the first practical useful high breakdown estimator
of multivariate location and dispersion.
See "Robustifying Robust Estimators" or "Applied Robust Statistics" for proofs.
- Olive, D.J. (2004), A Resistant Estimator of Multivariate Location and Dispersion,
Computational Statistics and Data Analysis, 46, 99-102.
rcov.pdf
-
- The following paper suggests ways to robustify regression techniques for single index models
and sliced inverse regression.
- Olive, D.J. (2004), Visualizing 1D Regression, in
Theory and Applications of Recent Robust Methods, edited by M. Hubert, G. Pison, A. Struyf and
S. Van Aelst, Series: Statistics for Industry and Technology, Birkhauser, Basel, 221-233.
vreg.pdf
-
- Olive, D.J., and Hawkins, D.M. (2003), Robust Regression with High Coverage,
Statistics and Probability Letters, 63, 259-266.
hcov.pdf
-
- The following paper provides a simultaneous diagnostic for whether the data
follows a multivariate normal distribution or some other elliptically contoured distribution.
It also provides a nice way to estimate and visualize single index models.
- Olive, D.J. (2002), Applications of Robust Distances for Regression, Technometrics, 44, 64-71.
rdist.pdf
-
- The following paper gives extremely important theoretical results.
It shows that software implementations for estimators of robust regression and
robust multivariate location and dispersion tend to be inconsistent with zero breakdown value.
The commonly used elemental basic resampling algorithm draws K elemental sets. Each
elemental fit is inconsistent, so the final estimator is inconsistent, regardless
of how the algorithm chooses the elemental fit.
The CM, GS, LMS, LQD, LTS, maximum depth, MCD, MVE, one step GM and GR, projection, S, tau,
t type, and many other robust estimators are of little applied interest because they are
impractical to compute. The "Robustifying Robust Estimators" paper shows how modify some
algorithms so that the resulting regression estimators are easily computed sqrt n consistent
high breakdown estimators and the resulting multivariate location and dispersion estimators
are sqrt n consistent with high outlier resistance.
- Hawkins, D.M., and Olive, D.J. (2002), Inconsistency of Resampling Algorithms for High
Breakdown Regression Estimators and a New Algorithm (with discussion), Journal of the American
Statistical Association, 97, 136-148.
incon.pdf
-
- This paper gives a graphical method for estimating response transformations
that can be used to complement or replace the numerical Box-Cox method.
- Cook, R.D., and Olive, D.J. (2001), A Note on Visualizing Response Transformations,
Technometrics, 43, 443-449. resp.pdf
-
- Olive, D.J. (2001), High Breakdown Analogs of the Trimmed Mean, Statistics and Probability
Letters, 51, 87-92.rloc.pdf
-
- Hawkins, D.M., and Olive, D.J. (1999), Improved Feasible Solution Algorithms for
High Breakdown Estimation, Computational Statistics and Data Analysis, 30, 1-11.
ifsa.pdf
-
- Hawkins, D.M., and Olive, D. (1999), Applications and Algorithms for Least Trimmed Sum
of Absolute Deviations Regression, Computational Statistics and Data Analysis, 32, 119-134.
lta.pdf
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