334 Hanes Hall
B.Sc. (1979), Cornell University
M.A. (1980), Yale University
M.Phil. (1983), Yale University
Ph.D. (1984), Yale University
Honors and Awards
Vicki & David Craver Academic Leadership Grant (2013)
Tanner Award for Excellence in Undergraduate Teaching (1997)
Senator Irving M. Ives Award (1977)
Senator Irving M. Ives Award (1976)
Alpha Lambda Delta Honor Society (1976)
Faculty Positions at U.N.C. – Chapel Hill
Professor, Department of Statistics & Operations Research (2003 – present)
Chairman, Department of Statistics & Operations Research (2009 – 2014)
Professor, Department of Statistics (1995 – 2003)
Interim Chairman, Department of Statistics (2002 – 2003)
Associate Professor, Department of Statistics (1990 – 1995)
Assistant Professor, Department of Statistics (1984 – 1990)
Carlstein’s main research interests are in methods of nonparametric statistical inference, that is, methods which do not require the user to know what particular distribution or model produced the data at hand. Such methods are needed when the statistician lacks prior knowledge of the underlying data-generating process, or when the statistician wants a robust corroborator for results from a parametric analysis of the data. He is especially interested in nonparametric estimation of change-points and boundaries, and of sampling distributions (via resampling).
A change-point is the time at which observations in a sequence cease to arise from the “old” distribution and begin to arise from a “new” distribution; nonparametric estimation of change-points is important in quality control and in epidemiology. When observations are on a grid, as in image-analysis or geological data, a boundary may partition the observations into homogeneous groups; this boundary can be estimated nonparametrically using methods analogous to the change-point estimators.
In order to make statistical inferences, one needs information about the sampling distribution of the statistic at hand. Although in many situations the sampling distribution is known to be approximately normal, there are many other cases where the sampling distribution cannot be derived theoretically, and may be quite non-normal, for example if the statistic is extremely complicated or if the observations are not independent. Resampling methods, such as the jackknife and the bootstrap, allow the statistician to nonparametrically estimate sampling distributions in these difficult situations, essentially by re-using the observed data.
The Use of Subseries Values for Estimating the Variance of a General Statistic from a Stationary Sequence, The Annals of Statistics, 14 (1986), 1171-1179.
[846 citations: Google Scholar]
Asymptotic Normality for a General Statistic from a Stationary Sequence, The Annals of Probability, 14 (1986), 1371-1379.
Simultaneous Confidence Regions for Predictions, The American Statistician, 40 (1986), 277-279.
Measures of Similarity Among Fuzzy Concepts: A Comparative Analysis, International Journal of Approximate Reasoning, 1 (1987), 221-242 (with R. Zwick, D. Budescu).
[622 citations: Google Scholar]
Nonparametric Change-Point Estimation, The Annals of Statistics, 16 (1988), 188-197.
[242 citations: Google Scholar]
Boundary Estimation, Journal of the American Statistical Association, 87 (1992), 430-438 (with C. Krishnamoorthy).
Nonparametric Estimation of the Moments of a General Statistic Computed from Spatial Data, Journal of the American Statistical Association, 89 (1994), 496-500 (with M. Sherman).
Nonparametric Change-Point Estimation for Data from an Ergodic Sequence, Theory of Probability and its Applications, 38 (1994), 726-733 (with S. Lele).
Change-Point Problems, IMS Lecture Notes Monograph Series, Volume 23 (1994), vii+385 pages (Co-Editor, with H.-G. Muller, D. Siegmund).
Replicate Histograms, Journal of the American Statistical Association, 91 (1996), 566-576 (with M. Sherman).
Matched-Block Bootstrap for Dependent Data, Bernoulli, 4 (1998), 305-328 (with K. Do, P. Hall, T. Hesterberg, H. Kunsch).
[133 citations: Google Scholar]
Confidence Intervals Based on Estimators with Unknown Rates of Convergence, Computational Statistics and Data Analysis, 46 (2004), 123-139 (with M. Sherman).