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Show Results For
- All HBS Web
(853)
- News (79)
- Research (640)
- Events (14)
- Multimedia (4)
- Faculty Publications (634)
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- 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... View Details
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. View Details
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. View Details
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. View Details
- 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... View Details
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... View Details
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.
- 03 Aug 2015
- Research & Ideas
Why Fierce Competitors Apple and Amazon Became ’Frenemies’ Over eReaders
researchers use a complex mathematical model to get to the bottom of just why enemies might decide to share a locker. It boils down to a difference in how they make their money. "Even though both [companies] make money from hardware and... View Details
- Article
Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness
By: Michael J Kearns, Seth Neel, Aaron Leon Roth and Zhiwei Steven Wu
The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier (like classification rate or false positive rate) across these groups.... View Details
Kearns, Michael J., Seth Neel, Aaron Leon Roth, and Zhiwei Steven Wu. "Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness." Proceedings of the International Conference on Machine Learning (ICML) 35th (2018).
- 2020
- Working Paper
Design and Analysis of Switchback Experiments
By: Iavor I Bojinov, David Simchi-Levi and Jinglong Zhao
In switchback experiments, a firm sequentially exposes an experimental unit to a random treatment, measures its response, and repeats the procedure for several periods to determine which treatment leads to the best outcome. Although practitioners have widely adopted... View Details
Bojinov, Iavor I., David Simchi-Levi, and Jinglong Zhao. "Design and Analysis of Switchback Experiments." Harvard Business School Working Paper, No. 21-034, September 2020.
- October 1992
- Case
Charles River Jazz Festival
Charles River Jazz Festival must decide whether to press a compact disk (CD) of Friday's jazz performance for sale on Saturday and Sunday. The idea to press CDs is novel, so there is considerable uncertainty about how receptive customers will be. The festival must... View Details
Wu, George. "Charles River Jazz Festival." Harvard Business School Case 893-004, October 1992.
- January 1982
- Background Note
Sharing Costs: Internal Telephone Billing Rates
By: Elon Kohlberg
Kohlberg, Elon. "Sharing Costs: Internal Telephone Billing Rates." Harvard Business School Background Note 182-109, January 1982.
- 2002
- Chapter
Future Possibilities in Finance Theory and Finance Practice
By: Robert C. Merton
Merton, Robert C. "Future Possibilities in Finance Theory and Finance Practice." In Mathematical Finance - Bachelier Congress 2000, edited by H. Geman, D. Madan, S. Pliska, and T. Vorst. Berlin: Springer-Verlag, 2002. (Was HBS Working Paper 01-030.)
- September 1976 (Revised June 1977)
- Background Note
Assessing Certainty Equivalents by Assessing Preference for Consequences
By: Paul A. Vatter
Vatter, Paul A. "Assessing Certainty Equivalents by Assessing Preference for Consequences." Harvard Business School Background Note 177-038, September 1976. (Revised June 1977.)