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  • All HBS Web  (840)
    • News  (79)
    • Research  (641)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (635)

Show Results For

  • All HBS Web  (840)
    • News  (79)
    • Research  (641)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (635)
← Page 12 of 840 Results →
  • 2021
  • Working Paper

How Much Should We Trust Staggered Difference-In-Differences Estimates?

By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
Difference-in-differences analysis with staggered treatment timing is frequently used to assess the impact of policy changes on corporate outcomes in academic research. However, recent advances in econometric theory show that such designs are likely to be biased in the... View Details
Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods
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Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered Difference-In-Differences Estimates?" European Corporate Governance Institute Finance Working Paper, No. 736/2021, February 2021. (Harvard Business School Working Paper, No. 21-112, April 2021.)
  • 1990
  • Chapter

Refinement of Nash Equilibrium: The Main Ideas

By: E. Kohlberg
Keywords: Mathematical Methods
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Kohlberg, E. "Refinement of Nash Equilibrium: The Main Ideas." In Game Theory and Applications, edited by T. Ichiishi, A. Neyman, and Y. Tauman. San Diego: Academic Press, 1990.
  • Article

Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80

By: Noam D. Elkies and Scott Duke Kominers
We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated by their vectors of norms... View Details
Keywords: Mathematical Methods
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Elkies, Noam D., and Scott Duke Kominers. "Refined Configuration Results for Extremal Type II Lattices of Ranks 40 and 80." Proceedings of the American Mathematical Society 138, no. 1 (January 2010): 105–108.
  • June 2006 (Revised March 2007)
  • Teaching Note

Polyphonic HMI: Mixing Music and Math

By: Anita Elberse
Keywords: Mathematical Methods; Music Industry
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Elberse, Anita. "Polyphonic HMI: Mixing Music and Math." Harvard Business School Teaching Note 506-081, June 2006. (Revised March 2007.)
  • February 2006
  • Teaching Note

Cost-Volume-Profit Models (TN)

By: David F. Hawkins, V.G. Narayanan, Michele Jurgens and Jacob Cohen
Keywords: Mathematical Methods
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Hawkins, David F., V.G. Narayanan, Michele Jurgens, and Jacob Cohen. "Cost-Volume-Profit Models (TN)." Harvard Business School Teaching Note 106-046, February 2006.
  • August 2005 (Revised April 2008)
  • Teaching Note

Store24 (A): Statistics Review with Data Desk (TN)

By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
Keywords: Mathematical Methods; Retail Industry
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Frei, Frances X. "Store24 (A): Statistics Review with Data Desk (TN)." Harvard Business School Teaching Note 606-036, August 2005. (Revised April 2008.)
  • 2006
  • Chapter

Advanced Regression Models

By: Raghuram Iyengar and Sunil Gupta
Keywords: Mathematical Methods
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Iyengar, Raghuram, and Sunil Gupta. "Advanced Regression Models." In Handbook of Marketing Research, edited by Rajiv Grover. Sage Publications, 2006.
  • 1978
  • Chapter

Matrix-Weighted Averages: Computation and Presentation

By: Dutch Leonard
Keywords: Mathematical Methods
Citation
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Leonard, Dutch. "Matrix-Weighted Averages: Computation and Presentation." In Proceedings of the Eleventh Symposium on the Interface of Computers and Statistics, edited by Ronald A. Gallant and Thomas Michael Gerig. Raleigh, NC: North Carolina State University, Institute of Statistics, 1978.
  • July 1982 (Revised March 1984)
  • Background Note

Worked Examples in Dynamic Programming

By: David E. Bell
Keywords: Mathematical Methods
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Bell, David E. "Worked Examples in Dynamic Programming." Harvard Business School Background Note 183-028, July 1982. (Revised March 1984.)
  • Web

Introduction - Option Pricing in Theory & Practice: The Nobel Prize Research of Robert C. Merton - Exhibits - Historical Collections

more than twenty-five years ago to the impact and growth of his groundbreaking work in the current academic and financial communities. The Black-Scholes option pricing model established the everyday use of mathematical models as essential... View Details
  • 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
Keywords: by Michael Blanding; Information; Publishing; Technology
  • Profile

Sid Shenai

For most of his life, Sid Shenai had pursued a single goal: to be a mathematical physicist. At Harvard, Sid finished his required courses early and participated in graduate level research. But his path toward a Ph.D was interrupted by a... View Details
  • 01 Mar 2005
  • News

Robert Buzzell Remembered

wholesale distribution; strategic planning; and the application of mathematical and statistical methods to marketing issues. A member of the HBS faculty from 1961 to 1993 and chair of the Marketing faculty from 1972 to 1977, he taught... View Details
  • Alumni WDYDWYD

Margaret Regan

education was definitely emphasized by my dad as a vehicle to growth and expanding my horizons. I got a BS in Mathematics and then worked in computer programming before managing the computer facility at a major company. That sounds like... View Details
  • Web

Fellows | MBA

Cohort 7 Isabella Mandis Statistics Lowell 2026 Cohort 7 Sean Meng Neuroscience Currier 2026 Cohort 7 Adam Zhou AB Computer Science, AB Economics, SM Computer Science Dunster 2025 Cohort 7 Alumni Rhea Acharya Applied Mathematics Eliot... View Details
  • 1972
  • Chapter

Random Walks and Technical Theories: Some Additional Evidence

By: George A. Benington and Michael C. Jensen
Keywords: Mathematical Methods
Citation
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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
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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
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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... View Details
Keywords: Mathematical Methods
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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... View Details
Keywords: Machine Learning Models; Counterfactual Explanations; Adversarial Examples; Mathematical Methods
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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).
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