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(838)
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Show Results For
- All HBS Web
(838)
- News (79)
- Research (640)
- Events (14)
- Multimedia (4)
- Faculty Publications (632)
- March 2022
- Article
Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models
By: Fiammetta Menchetti and Iavor Bojinov
Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless... View Details
Keywords: Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods
Menchetti, Fiammetta, and Iavor Bojinov. "Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models." Annals of Applied Statistics 16, no. 1 (March 2022): 414–435.
- 2021
- Working Paper
Population Interference in Panel Experiments
By: Iavor I Bojinov, Kevin Wu Han and Guillaume Basse
The phenomenon of population interference, where a treatment assigned to one experimental unit affects another experimental unit's outcome, has received considerable attention in standard randomized experiments. The complications produced by population interference in... View Details
Bojinov, Iavor I., Kevin Wu Han, and Guillaume Basse. "Population Interference in Panel Experiments." Harvard Business School Working Paper, No. 21-100, March 2021.
- September 2021
- Article
Oh's 8-Universality Criterion Is Unique
Using the methods developed for the proof that the 2-universality criterion is unique, we partially characterize criteria for the n-universality of positive-definite integer-matrix quadratic forms. We then obtain the uniqueness of Oh’s 8-universality criterion as an... View Details
Keywords: N-universal Lattice; 8-universal Lattice; Universality Criteria; Quadratic Forms; Additively Indecomposable; Mathematical Methods
Kominers, Scott Duke. "Oh's 8-Universality Criterion Is Unique." Kyungpook Mathematical Journal 61, no. 3 (September 2021): 455–459.
- 2021
- Article
Prisoners, Rooms, and Lightswitches
By: Daniel M. Kane and Scott Duke Kominers
We examine a new variant of the classic prisoners and lightswitches puzzle: A warden leads his n prisoners in and out of r rooms, one at a time, in some order, with each prisoner eventually visiting every room an arbitrarily large number of times. The... View Details
Keywords: Mathematical Methods
Kane, Daniel M., and Scott Duke Kominers. "Prisoners, Rooms, and Lightswitches." Electronic Journal of Combinatorics 28, no. 1 (2021).
- 2019
- Article
Configurations of Extremal Type II Codes via Harmonic Weight Enumerators
By: Noam D. Elkies and Scott Duke Kominers
We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes via Harmonic Weight Enumerators." Journal de Théorie des Nombres de Bordeaux 31, no. 3 (2019): 679–688.
- 2019
- Article
Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading
By: Iavor I Bojinov and Neil Shephard
We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data. Our approach allows the estimation of a broad class of these estimands and exact randomization based p-values for testing causal... View Details
Bojinov, Iavor I., and Neil Shephard. "Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading." Journal of the American Statistical Association 114, no. 528 (2019): 1665–1682.
- Article
A New Proof of Serre's Homological Characterization of Regular Local Rings
By: Ravi Jagadeesan and Aaron Landesman
We give a new proof of Serre’s result that a Noetherian local ring is regular if and only if it has finite global dimension. Our proof avoids the explicit construction of a Koszul complex. View Details
Keywords: Mathematical Methods
Jagadeesan, Ravi, and Aaron Landesman. "A New Proof of Serre's Homological Characterization of Regular Local Rings." Art. 18. Research in Number Theory 2 (December 2016).
- October 2015
- Article
A New Gal(ℚ^⎯/ℚ)-invariant of Dessins d'enfants
By: Ravi Jagadeesan
We study the action of Gal(ℚ^⎯/ℚ) on the category of Belyĭ functions (finite étale covers of ℙ^1_(ℚ^⎯) \ {0,1,∞}. We describe a new combinatorial Gal(ℚ^⎯/ℚ)‐invariant for Belyĭ functions whose monodromy cycle types above 0 and ∞ are the same. We use a version of our... View Details
Keywords: Mathematical Methods
Jagadeesan, Ravi. "A New Gal(ℚ^⎯/ℚ)-invariant of Dessins d'enfants." Proceedings of the London Mathematical Society 111, no. 4 (October 2015): 911–935.
- 2014
- Article
Ascent-Descent Young Diagrams and Pattern Avoidance in Alternating Permutations
By: Ravi Jagadeesan
We investigate pattern avoidance in alternating permutations and an alternating analogue of Young diagrams. In particular, using an extension of Babson and West’s notion of shape-Wilf equivalence described in our recent paper (with N. Gowravaram), we generalize results... View Details
Jagadeesan, Ravi. "Ascent-Descent Young Diagrams and Pattern Avoidance in Alternating Permutations." #P3.9. Electronic Journal of Combinatorics 21, no. 3 (2014).
- 2018
- Working Paper
Semi-Parametric Estimation of Dynamic Discrete Choice Models
By: David Hao Zhang
I develop a new method for estimating counterfactuals in dynamic discrete choice models, a widely used set of models in economics, without requiring a distributional assumption on utility shocks. Applying my method to the canonical Rust (1987) setting, I find that the... View Details
Zhang, David Hao. "Semi-Parametric Estimation of Dynamic Discrete Choice Models." Working Paper, April 2018.
- January 2016
- Article
Zooming In: A Practical Manual for Identifying Geographic Clusters
By: Juan Alcacer and Minyuan Zhao
This paper takes a close look at the reasons, procedures, and results of cluster identification methods. Despite being a popular research topic in strategy, economics, and sociology, geographic clusters are often studied with little consideration given to the... View Details
Keywords: Mathematical Methods
Alcacer, Juan, and Minyuan Zhao. "Zooming In: A Practical Manual for Identifying Geographic Clusters." Strategic Management Journal 37, no. 1 (January 2016): 10–21.
- 2013
- Chapter
Weighted Generating Functions for Type II Lattices and Codes
By: Noam D. Elkies and Scott Duke Kominers
We give a new structural development of harmonic polynomials on Hamming space, and harmonic weight enumerators of binary linear codes, that parallels one approach to harmonic polynomials on Euclidean space and weighted theta functions of Euclidean lattices. Namely, we... View Details
Keywords: Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Weighted Generating Functions for Type II Lattices and Codes." In Quadratic and Higher Degree Forms. Vol. 31, edited by Alladi Krishnaswami, Manjul Bhargava, David Savitt, and Pham Huu Tiep, 63–108. Developments in Mathematics. Springer, 2013.
- Article
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
By: Daniel M. Kane and Scott Duke Kominers
For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained... View Details
Keywords: Mathematical Methods
Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
- 1987
- Chapter
Continuous-Time Stochastic Models
By: Robert C. Merton
Keywords: Mathematical Methods
Merton, Robert C. "Continuous-Time Stochastic Models." In The New Palgrave: A Dictionary of Economic Theory and Doctrine, edited by John Eatwell, Murray Milgate, and Peter Newman. London: Macmillan Press, 1987. (Revised in The New Palgrave Dictionary of Money and Finance, London: MacMillan Press, Ltd., 1992.)
- February 1996
- Exercise
Problems in Variance Analysis
By: William J. Bruns Jr.
Keywords: Mathematical Methods
Bruns, William J., Jr. "Problems in Variance Analysis." Harvard Business School Exercise 196-120, February 1996.
- May 1983
- Article
Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming
By: André Perold and R. Meidan
Keywords: Mathematical Methods
Perold, André, and R. Meidan. "Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming." Journal of Optimization Theory and Applications 40, no. 1 (May 1983): 61–76.
- February 2005 (Revised November 2006)
- Background Note
Using Data Desk for Statistical Analysis
By: Frances X. Frei and Dennis Campbell
Describes how to use the Data Desk software package to perform statistical analysis. View Details
Keywords: Mathematical Methods
Frei, Frances X., and Dennis Campbell. "Using Data Desk for Statistical Analysis." Harvard Business School Background Note 605-060, February 2005. (Revised November 2006.)
- March 2004
- Tutorial
Variance Analysis Tutorial
By: David F. Hawkins and Jacob Cohen
An interactive tutorial on variance analysis, flexible budgets, and overhead allocation. View Details
Keywords: Mathematical Methods
- 1977
- Article
On the Joint Distribution of Left- and Right-sided Outliner Statistics
By: André Perold and D. M. Hawkins
Keywords: Mathematical Methods
Perold, André, and D. M. Hawkins. "On the Joint Distribution of Left- and Right-sided Outliner Statistics." Utilitas mathematica 12 (1977): 129–143.