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(852)
- News (77)
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- Faculty Publications (633)
Show Results For
-
All HBS Web
(852)
- News (77)
- Research (635)
- Events (11)
- Multimedia (4)
- Faculty Publications (633)
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- Article
Matching in Networks with Bilateral Contracts: Corrigendum
By: John William Hatfield, Ravi Jagadeesan and Scott Duke Kominers
Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in...
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Hatfield, John William, Ravi Jagadeesan, and Scott Duke Kominers. "Matching in Networks with Bilateral Contracts: Corrigendum." American Economic Journal: Microeconomics 12, no. 3 (August 2020): 277–285.
- 1981
- Chapter
A Degeneracy Exploiting LU Factorization for the Simplex Method
By: André Perold
Keywords:
Mathematical Methods
- 2015
- Working Paper
Configurations of Extremal Type II Codes
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...
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Keywords:
Mathematical Methods
Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes." Working Paper, March 2015.
- February 1991 (Revised February 1993)
- Background Note
Regression Analysis
By: David E. Bell
Provides a relatively simple introduction to multivariate regression analysis.
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Keywords:
Mathematical Methods
Bell, David E. "Regression Analysis." Harvard Business School Background Note 191-117, February 1991. (Revised February 1993.)
- Article
Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)
By: Scott Duke Kominers and Zachary Abel
We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1.
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Keywords:
Mathematical Methods
Kominers, Scott Duke, and Zachary Abel. "Configurations of Rank-40r Extremal Even Unimodular Lattices (r=1,2,3)." Journal de Théorie des Nombres de Bordeaux 20, no. 2 (2008): 365–371.
- August 2005 (Revised April 2008)
- Teaching Note
Store24 (B): Statistics Review with Data Desk (TN)
By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion.
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- fall 1992
- Article
Exploring the Limits of the Technology S-curve, Part 1: Component Technologies
By: Clayton M. Christensen
Christensen, Clayton M. "Exploring the Limits of the Technology S-curve, Part 1: Component Technologies." Production and Operations Management 1 (fall 1992): 334–357.
- 20 Mar 2001 - 21 Mar 2001
- Conference Presentation
QAP: The Quadratic Assignment Procedure
By: William B. Simpson
Keywords:
Mathematical Methods
Simpson, William B. "QAP: The Quadratic Assignment Procedure." Paper presented at the North American Stata Users' Group Meeting, March 20–21, 2001.
- 2002
- Case
Qualitative Response Models: Ordinal and Multinomial Models
By: William B. Simpson
Keywords:
Mathematical Methods
Simpson, William B. "Qualitative Response Models: Ordinal and Multinomial Models." 2002. Electronic.
- 1979
- Dissertation
Inference in Partially Identified Models
By: Dutch Leonard
Keywords:
Mathematical Methods
- Article
The Shapley Value as a von Neumann-Morgenstern Utility
By: A. E. Roth
Roth, A. E. "The Shapley Value as a von Neumann-Morgenstern Utility." Econometrica 45, no. 3 (April 1977): 657–664.
- Article
Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns
By: Joel Goh, Kian Guan Lim, Melvyn Sim and Weina Zhang
We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using...
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Goh, Joel, Kian Guan Lim, Melvyn Sim, and Weina Zhang. "Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns." European Journal of Operational Research 221, no. 2 (September 1, 2012): 397–406.
- July 1985 (Revised March 1994)
- Background Note
Exposure and Hedging
By: David E. Bell
Describes the concept of exposure; the dependence of a goal on an uncertain external event. Describes in detail how hedges may be constructed to eliminate exposure, including the algebra of cross-hedging and hedge ratios. The relevance of regression analysis is...
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Bell, David E. "Exposure and Hedging." Harvard Business School Background Note 186-036, July 1985. (Revised March 1994.)
- 1976
- Book
Lies, Damn Lies and Statistics: The Manipulation of Public Opinion in America
Wheeler, Michael A. Lies, Damn Lies and Statistics: The Manipulation of Public Opinion in America. New York, NY: W. W. Norton & Company, 1976.
- 1972
- Chapter
Random Walks and Technical Theories: Some Additional Evidence
By: George A. Benington and Michael C. Jensen
Keywords:
Mathematical Methods
Benington, George A., and Michael C. Jensen. "Random Walks and Technical Theories: Some Additional Evidence." In Security Evaluation and Portfolio Analysis, edited by E. Elton and M. Gruber. Prentice Hall, 1972. (Also published in Journal of Finance (May 1970) and Investment Management: Some Readings, J. Lorie and R. Brealey, Editors (Praeger Publishers, 1972).)
- 1979
- Article
An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem
By: C. Blair and A. E. Roth
Keywords:
Mathematical Methods
Blair, C., and A. E. Roth. "An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem." Algebra Universalis 9 (1979): 131–132.
- January 1975
- Article
A Lattice Fixed-Point Theorem with Constraints
By: A. E. Roth
Keywords:
Mathematical Methods
Roth, A. E. "A Lattice Fixed-Point Theorem with Constraints." Bulletin of the American Mathematical Society 81 (January 1975): 136–138.
- September–October 2023
- Article
Interpretable Matrix Completion: A Discrete Optimization Approach
By: Dimitris Bertsimas and Michael Lingzhi Li
We consider the problem of matrix completion on an n × m matrix. We introduce the problem of interpretable matrix completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the problem can be...
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Keywords:
Mathematical Methods
Bertsimas, Dimitris, and Michael Lingzhi Li. "Interpretable Matrix Completion: A Discrete Optimization Approach." INFORMS Journal on Computing 35, no. 5 (September–October 2023): 952–965.
- 2022
- Article
Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis.
By: Martin Pawelczyk, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay and Himabindu Lakkaraju
As machine learning (ML) models become more widely deployed in high-stakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of counterfactual explanations, a...
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Keywords:
Machine Learning Models;
Counterfactual Explanations;
Adversarial Examples;
Mathematical Methods
Pawelczyk, Martin, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay, and Himabindu Lakkaraju. "Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis." Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) 25th (2022).
- November 2021
- Article
Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective
By: Iavor Bojinov, Ashesh Rambachan and Neil Shephard
In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative...
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Keywords:
Panel Data;
Dynamic Causal Effects;
Potential Outcomes;
Finite Population;
Nonparametric;
Mathematical Methods
Bojinov, Iavor, Ashesh Rambachan, and Neil Shephard. "Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective." Quantitative Economics 12, no. 4 (November 2021): 1171–1196.