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Efficient Computation of Confidence Sets Using Classification on Equidistributed Grids

Lujie Zhou

arXiv 3 Jan 2024 · Econometrics

arXiv:2401.01804 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Economic models produce moment inequalities, which can be used to form tests of the true parameters. Confidence sets (CS) of the true parameters are derived by inverting these tests. However, they often lack analytical expressions, necessitating a grid search to obtain the CS numerically by retaining the grid points that pass the test. When the statistic is not asymptotically pivotal, constructing the critical value for each grid point in the parameter space adds to the computational burden. In this paper, we convert the computational issue into a classification problem by using a support vector machine (SVM) classifier. Its decision function provides a faster and more systematic way of dividing the parameter space into two regions: inside vs. outside of the confidence set. We label those points in the CS as 1 and those outside as -1. Researchers can train the SVM classifier on a grid of manageable size and use it to determine whether points on denser grids are in the CS or not. We establish certain conditions for the grid so that there is a tuning that allows us to asymptotically reproduce the test in the CS. This means that in the limit, a point is classified as belonging to the confidence set if and only if it is labeled as 1 by the SVM.

Citation extraction

21
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appendix boundary found by appendix_command · 85% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Ciliberto, F. and Tamer, E (2009) Market structure and multiple equilibria in airline markets0.87452100%
2Chernozhukov, V., Hong, H., and Tamer, E (2007) Estimation and confidence regions for parameter sets in econometric models0.73732100%
3Rosen, A (2008) Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities0.58531100%
4Aradillas-Lopez, A. and Gandhi, A (2016) Estimation of games with ordered actions: An application to chain-store entry: Estimation of games with ordered actions0.51121100%
5Judd, K. L (1998) Numerical Methods in Economics, volume 1 of MIT Press Books0.51121100%
6Li, L. and Henry, M (2022) Finite Sample Inference in Incomplete Models0.51121100%
7Wu, H.-S. and Zhang, F.-M (2014) Wolf pack algorithm for unconstrained global optimization0.51121100%
8Andrews, I., Roth, J., and Pakes, A (2019) Inference for linear conditional moment inequalities0.40511100%
9Cortes, C. and Vapnik, V (1995) Support vector networks0.40511100%
10Hastie, T., Tibshirani, R., and Friedman, J (2001) The Elements of Statistical Learning0.40511100%

Showing the top 10 of 21 scored citations.