Dylan Small
- Class of 1965 Wharton Professor of Statistics
Contact Information
- Primary Email:
dsmall@wharton.upenn.edu - Office Phone:
(215) 573-5241
- office Address:
464 Jon M. Huntsman Hall
3730 Walnut Street
Philadelphia, PA 19104
Research Interests: applications of statistics to public health, design and analysis of experiments and observational studies for comparing treatments, longitudinal data, measurement error, medicine and economics
Links: Personal Website
Overview
Education
PhD, Stanford University, 2002
BA, Harvard University, 1997
Academic Positions Held
Wharton: 2002-present
For more information, go to My Personal Page
Research
Jennifer A. Faerber, Marshall M. Joffe, Dylan Small, Rongmei Zhang, Gregory K. Brown, Thomas R. Ten Have (2018), A Simple Model Allowing Modification of the Effect of a Randomized Intervention by Post-Randomization Variables, Journal of Causal Inference, 5 (2).
Zijian Guo, Hyunseung Kang, Tony Cai, Dylan Small (Forthcoming), Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting.
Abstract: The instrumental variable (IV) method is commonly used to estimate the causal effect of a treatment on an outcome by using IVs that satisfy the assumptions of association with treatment, no direct effect on the outcome and ignorability. A major challenge in IV analysis is to find said IVs, but typically one is unsure of whether all of the putative IVs are in fact valid (i.e. satisfy the assumptions). We propose a general inference procedure that provides honest inference in the presence of invalid IVs, even after controlling for a large number of covariates. The key step of our method is a novel selection procedure, which we call Two-Stage Hard Thresholding (TSHT), where we use hard thresholding to select the set of non-redundant instruments in the first stage and subsequently use hard thresholding to select the valid instruments in the second stage using the thresholding from the first stage. TSHT allows us to not only select invalid p IVs, but also provides honest confidence intervals of the treatment effect at $sqrt{n}$ rate. We establish asymptotic properties of our procedure and demonstrate that our procedure performs well in simulation studies compared to traditional IV methods, especially when the instruments are invalid.
Xuran Wang, Yang Jiang, Nancy Zhang, Dylan Small (2018), Sensitivity Analysis and Power for Instrumental Variable Studies, Biometrics, (in press).
Hal S. Stern, Daniel Blower, Michael L. Cohen, Charles A. Czeisler, David F. Dinges, Joel B. Greenhouse, Feng Guo, Richard J. Hanowski, Natalie P. Hartenbaum, Gerald P. Krueger, Melissa M. Mallis, Richard F. Pain, Matthew Rizzo, Esha Sinha, Dylan Small, Elizabeth A. Stuart, David H. Wegman (2018), Data and Methods for Studying Commercial Motor Vehicle Driver Fatigue, Highway Safety and Long-Term Driver Health, Accident Analysis & Prevention, (in press).
Ashkan Ertefaie, Dylan Small, Paul R. Rosenbaum (2018), Quantitative evaluation of the trade-off of strengthened instruments and sample size in observational studies, Journal of the American Statistical Association, (in press).
Qingyuan Zhao, Dylan Small, Paul R. Rosenbaum (2018), Cross-screening in observational studies that test many hypotheses, Journal of the American Statistical Association, (in press).
Mitesh S. Patel, Kevin G. Volpp, Roy Rosin, Scarlett L. Bellamy, Dylan Small, Jack Heuer, Susan Sproat, Chris Hyson, Nancy Haff, Samantha M. Lee, Lisa Wesby, Karen Hoffer, David Shuttleworth, Devon H. Taylor, Victoria Hilbert, Jingsan Zhu, Lin Yang, Xingmei Wang, David A. Asch (2018), A Randomized, Controlled Trial of Lottery-Based Financial Incentives to Increase Physical Activity Among Overweight and Obese Adults, American Journal of Health Promotion, (in press).
Qingyuan Zhao and Dylan Small (2018), Graphical Diagnosis of Confounding Bias in Instrumental Variable Analysis, Epidemiology, 29(4):e29–e31.
Fei Wan, Dylan Small, Nandita Mitra (2018), A General Approach to Evaluating the Bias of 2‐Stage Instrumental Variable Estimators, Statistics in Medicine, 37 (12), pp. 1997-2015.
Elinore J. Kaufman, Ashkan Ertefaie, Dylan Small, Daniel N. Holena, M. Kit Delgado (2018), Comparative Effectiveness of Initial Treatment at Trauma Center vs Neurosurgery-Capable Non-Trauma Center for Severe, Isolated Head Injury, Journal of the American College of Surgeons, 226(5):741-751.e2.
Teaching
Past Courses
STAT101 - INTRO BUSINESS STAT
Data summaries and descriptive statistics; introduction to a statistical computer package; Probability: distributions, expectation, variance, covariance, portfolios, central limit theorem; statistical inference of univariate data; Statistical inference for bivariate data: inference for intrinsically linear simple regression models. This course will have a business focus, but is not inappropriate for students in the college.
STAT102 - INTRO BUSINESS STAT
Continuation of STAT 101. A thorough treatment of multiple regression, model selection, analysis of variance, linear logistic regression; introduction to time series. Business applications.
STAT112 - INTRODUCTORY STATISTICS
Further development of the material in STAT 111, in particular the analysis of variance, multiple regression, non-parametric procedures and the analysis of categorical data. Data analysis via statistical packages.
STAT475 - SAMPLE SURVEY DESIGN
This course will cover the design and analysis of sample surveys. Topics include simple sampling, stratified sampling, cluster sampling, graphics, regression analysis using complex surveys and methods for handling nonresponse bias.
STAT490 - CAUSAL INFERENCE
Questions about cause are at the heart of many everyday decisions and public policies. Does eating an egg every day cause people to live longer or shorter or have no effect? Do gun control laws cause more or less murders or have no effect? Causal inference is the subfield of statistics that considers how we should make inferences about such questions. This course will cover the key concepts and methods of causal inference rigorously. The course is intended for statistics concentrators and minors.
STAT510 - PROBABILITY
Elements of matrix algebra. Discrete and continuous random variables and their distributions. Moments and moment generating functions. Joint distributions. Functions and transformations of random variables. Law of large numbers and the central limit theorem. Point estimation: sufficiency, maximum likelihood, minimum variance. Confidence intervals.
STAT512 - MATHEMATICAL STATISTICS
An introduction to the mathematical theory of statistics. Estimation, with a focus on properties of sufficient statistics and maximum likelihood estimators. Hypothesis testing, with a focus on likelihood ratio tests and the consequent development of "t" tests and hypothesis tests in regression and ANOVA. Nonparametric procedures.
STAT520 - APPLIED ECONOMETRICS I
This is a course in econometrics for graduate students. The goal is to prepare students for empirical research by studying econometric methodology and its theoretical foundations. Students taking the course should be familiar with elementary statistical methodology and basic linear algebra, and should have some programming experience. Topics include conditional expectation and linear projection, asymptotic statistical theory, ordinary least squares estimation, the bootstrap and jackknife, instrumental variables and two-stage least squares, specification tests, systems of equations, generalized least squares, and introduction to use of linear panel data models.
STAT521 - APPLIED ECONOMETRICS II
Topics include system estimation with instrumental variables, fixed effects and random effects estimation, M-estimation, nonlinear regression, quantile regression, maximum likelihood estimation, generalized method of moments estimation, minimum distance estimation, and binary and multinomial response models. Both theory and applications will be stressed.
STAT590 - CAUSAL INFERENCE
Questions about cause are at the heart of many everyday decisions and public policies. Does eating an egg every day cause people to live longer or shorter or have no effect? Do gun control laws cause more or less murders or have no effect? Causal inference is the subfield of statistics that considers how we should make inferences about such questions. This course will cover the key concepts and methods of causal inference rigorously.
STAT920 - SAMPLE SURVEY METHODS
This course will cover the design and analysis of sample surveys. Topics include simple random sampling, stratified sampling, cluster sampling, graphics, regression analysis using complex surveys and methods for handling nonresponse bias.
STAT921 - OBSERVATIONAL STUDIES
This course will cover statistical methods for the design and analysis of observational studies. Topics will include the potential outcomes framework for causal inference; randomized experiments; matching and propensity score methods for controlling confounding in observational studies; tests of hidden bias; sensitivity analysis; and instrumental variables.
STAT962 - ADV METHODS APPLIED STAT
This course is designed for Ph.D. students in statistics and will cover various advanced methods and models that are useful in applied statistics. Topics for the course will include missing data, measurement error, nonlinear and generalized linear regression models, survival analysis, experimental design, longitudinal studies, building R packages and reproducible research.
STAT970 - MATHEMATICAL STATISTICS
Decision theory and statistical optimality criteria, sufficiency, point estimation and hypothesis testing methods and theory.
STAT971 - INTRO TO LINEAR STAT MOD
Theory of the Gaussian Linear Model, with applications to illustrate and complement the theory. Distribution theory of standard tests and estimates in multiple regression and ANOVA models. Model selection and its consequences. Random effects, Bayes, empirical Bayes and minimax estimation for such models. Generalized (Log-linear) models for specific non-Gaussian settings.
STAT991 - SEM IN ADV APPL OF STAT
This seminar will be taken by doctoral candidates after the completion of most of their coursework. Topics vary from year to year and are chosen from advance probability, statistical inference, robust methods, and decision theory with principal emphasis on applications.
STAT995 - DISSERTATION
STAT999 - INDEPENDENT STUDY
Awards and Honors
- Fellow, American Statistical Association, 2013
In the News
Knowledge @ Wharton
- Sports and Statistics: Correlating Football to Brain Injury, Knowledge @ Wharton - 07/21/2017
- Are Your Customers ‘Clumpy’? What Binge-buying Means for Marketers, Knowledge @ Wharton - 12/17/2014
- Bound for the Beach? Bring These Books…, Knowledge @ Wharton - 06/26/2012
Activity
Latest Research
In the News
Sports and Statistics: Correlating Football to Brain InjuryNew Wharton research examines the long-term impact of playing high school or college football.
Knowledge @ Wharton - 2017/07/21