Andreas Buja

• Andreas Buja and Wolfgang Rolke (Work In Progress), Calibration for Simultaneity: (Re)sampling Methods for Simultaneous Inference with Applications to Function Estimation and Functional Data. Abstract

  We survey and illustrate a Monte Carlo technique for carrying out simple simultaneous inference with arbitrarily many statistics. Special cases of the technique have appeared in the literature, but there exists widespread unawareness of the simplicity and broad applicability of this solution to simultaneous inference.
  The technique, here called “calibration for simultaneity” or CfS , consists of 1) limiting the search for coverage regions to a one-parameter family of nested regions, and 2) selecting from the family that region whose estimated coverage probability has the desired value. Natural one-parameter families are almost always available.
  CfS applies whenever inference is based on a single distribution, for example: 1) fixed distributions such as Gaussians when diagnosing distributional assumptions, 2) conditional null distributions in exact tests with Neyman structure, in particular permutation tests, 3) bootstrap distributions for bootstrap standard error bands, 4) Bayesian posterior distributions for high-dimensional posterior probability regions, or 5) predictive distributions for multiple prediction intervals.
  CfS is particularly useful for estimation of any type of function, such as empirical Q-Q curves, empirical CDFs, density estimates, smooths, generally any type of _t, and functions estimated from functional data.
  A special case of CfS is equivalent to p-value adjustment (Westfall and Young, 1993). Conversely, the notion of a p-value can be extended to any simultaneous coverage problem that is solved with a one-parameter family of coverage regions.

• Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja, Edward I. George, Linda Zhao (2021), Uniform-in-Submodel Bounds for Linear Regression in a Model Free Framework, Econometric Theory, (in press) ().
• Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja, Edward I. George, Linda Zhao (2020), A Model Free Perspective for Linear Regression: Uniform-in-model Bounds for Post Selection Inference, Econometric Theory, (to appear) (). Abstract

  For the last two decades, high-dimensional data and methods have proliferated
  throughout the literature. The classical technique of linear regression, however, has not lost
  its touch in applications. Most high-dimensional estimation techniques can be seen as variable
  selection tools which lead to a smaller set of variables where classical linear regression
  technique applies. In this paper, we prove estimation error and linear representation bounds
  for the linear regression estimator uniformly over (many) subsets of variables. Based on deterministic
  inequalities, our results provide “good” rates when applied to both independent
  and dependent data. These results are useful in correctly interpreting the linear regression
  estimator obtained after exploring the data and also in post model-selection inference. All
  the results are derived under no model assumptions and are non-asymptotic in nature.

• Richard A. Berk, Andreas Buja, Lawrence D. Brown, Edward I. George, Arun Kumar Kuchibhotla, Weijie Su, Linda Zhao (2020), Assumption Lean Regression, American Statistician, (in press) ().
• Richard A. Berk, Matthew Olson, Andreas Buja, Aurelie Ouss (2020), Using Recursive Partitioning to Find and Estimate Heterogenous Treatment Effects in Randomized Clinical Trials, Journal of Experimential Criminology, (to appear) ().
• Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja, Edward I. George, Linda Zhao (2020), Valid Post-selection Inference in Model-free Linear Regression, Annals of Statistics, 48 (5), pp. 2953-2981. Abstract

  This paper provides multiple approaches to perform valid post-selection inference in an assumption-lean regression analysis. To the best of our knowledge, this is the first work that provides valid post-selection inference for regression analysis in such a general settings that include independent, m-dependent random variables.

  Related
  Files

  Supplement to Valid post-selection inference
• Andreas Buja, Arun Kumar Kuchibhotla, Richard A. Berk, Edward I. George, Eric Tchetgen Tchetgen, Linda Zhao (2020), Models as Approximations—Rejoinder, Statistical Science, 34 (4), pp. 606-620.
• Andreas Buja, Lawrence D. Brown, Richard A. Berk, Edward I. George, Emil Pitkin, Mikhail Traskin, Kai Zhang, Linda Zhao (2019), Models as Approximations I: Consequences Illustrated with Linear Regression, Statistical Science, 34 (4), pp. 523-544.
• Andreas Buja, Lawrence D. Brown, Arun Kumar Kuchibhotla, Richard A. Berk, Edward I. George, Linda Zhao (2019), Models as Approximations II: A Model-Free Theory of Parametric Regression, Statistical Science, 34 (4), pp. 345-365.
• Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja, Junhui Cai (Working), All of Linear Regression.
• All Research from Andreas Buja »

Past Courses

• STAT3990 - Independent Study

  Written permission of instructor and the department course coordinator required to enroll in this course.

• STAT4700 - Data Analy & Stat Comp

  This course will introduce a high-level programming language, called R, that is widely used for statistical data analysis. Using R, we will study and practice the following methodologies: data cleaning, feature extraction; web scrubbing, text analysis; data visualization; fitting statistical models; simulation of probability distributions and statistical models; statistical inference methods that use simulations (bootstrap, permutation tests). Prerequisite: Waiving the Statistics Core completely if prerequisites are not met. This course may be taken concurrently with the prerequisite with instructor permission.

• STAT5030 - Data Analy & Stat Comp

  This course will introduce a high-level programming language, called R, that is widely used for statistical data analysis. Using R, we will study and practice the following methodologies: data cleaning, feature extraction; web scrubbing, text analysis; data visualization; fitting statistical models; simulation of probability distributions and statistical models; statistical inference methods that use simulations (bootstrap, permutation tests). Prerequisite: Two courses at the statistics 4000 or 5000 level.

• STAT7700 - Data Analy & Stat Comp

  This course will introduce a high-level programming language, called R, that is widely used for statistical data analysis. Using R, we will study and practice the following methodologies: data cleaning, feature extraction; web scrubbing, text analysis; data visualization; fitting statistical models; simulation of probability distributions and statistical models; statistical inference methods that use simulations (bootstrap, permutation tests). Prerequisite: Two courses at the statistics 4000 or 5000 level.

• STAT9260 - Multivariate Analy: Meth

  This is a course that prepares PhD students in statistics for research in multivariate statistics and data visualization. The emphasis will be on a deep conceptual understanding of multivariate methods to the point where students will propose variations and extensions to existing methods or whole new approaches to problems previously solved by classical methods. Topics include: principal component analysis, canonical correlation analysis, generalized canonical analysis; nonlinear extensions of multivariate methods based on optimal transformations of quantitative variables and optimal scaling of categorical variables; shrinkage- and sparsity-based extensions to classical methods; clustering methods of the k-means and hierarchical varieties; multidimensional scaling, graph drawing, and manifold estimation.

• STAT9610 - Statistical Methodology

  This is a course that prepares 1st year PhD students in statistics for a research career. This is not an applied statistics course. Topics covered include: linear models and their high-dimensional geometry, statistical inference illustrated with linear models, diagnostics for linear models, bootstrap and permutation inference, principal component analysis, smoothing and cross-validation.

• STAT9950 - Dissertation

  Dissertation

• STAT9990 - Independent Study

  Written permission of instructor and the department course coordinator required to enroll.

• Keynote speaker, Classification Society Conference, Milwaukee, WI, USA, 2013
• Infovis best paper award for the article ``Graphical inference for infovis'' by Wickham, H., Cook, D., Hofmann, H., and Buja, A. IEEE Transactions on Visualization and Computer Graphics (Proc. InfoVis'10)., 2010
• Journal of Marketing, finalist for the Harold H. Maynard Award and featured blog article of the October Issue, 2007
• Keynote speaker, SIAM Conference on Datamining (SDM06), Bethesda, MD, USA, 2006
• Fellow, Institute of Mathematical Statistics, 2006
• IMS Medallion lecture, Joint Statistical Meetings, New York, 2002
• Keynote speaker, European Meeting of the Psychometric Society, Leiden, 1995
• Fellow, American Statistical Association, 1994
• Award Medal for diploma thesis in mathematics, Swiss Federal Institute of Technology, 1975

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