arXiv 4 Feb 2024 · Mathematics — Statistics Theory
arXiv:2402.02303 · PDF · DOI · OpenAlex · Extracted main text
The linear Fisher market (LFM) is a basic equilibrium model from economics, which also has applications in fair and efficient resource allocation. First-price pacing equilibrium (FPPE) is a model capturing budget-management mechanisms in first-price auctions. In certain practical settings such as advertising auctions, there is an interest in performing statistical inference over these models. A popular methodology for general statistical inference is the bootstrap procedure. Yet, for LFM and FPPE there is no existing theory for the valid application of bootstrap procedures. In this paper, we introduce and devise several statistically valid bootstrap inference procedures for LFM and FPPE. The most challenging part is to bootstrap general FPPE, which reduces to bootstrapping constrained M-estimators, a largely unexplored problem. We devise a bootstrap procedure for FPPE under mild degeneracy conditions by using the powerful tool of epi-convergence theory. Experiments with synthetic and semi-real data verify our theory.
appendix boundary found by appendix_command · 40% of the source is main text. Read the extracted text to check this.
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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Conitzer, V., Kroer, C., Panigrahi, D., Schrijvers, O., Stier-Moses,… (2022) Pacing equilibrium in first price auction markets self | 0.950 | 7 | 3 | 86% |
| 2 | Li, J (2023) The proximal bootstrap for constrained estimators | 0.851 | 13 | 5 | 62% |
| 3 | Liao, L. and Kroer, C (2023) Statistical Inference and A/B Testing for First-Price Pacing Equilibria self | 0.825 | 16 | 5 | 56% |
| 4 | Shapiro, A (1989) Asymptotic properties of statistical estimators in stochastic programming | 0.811 | 4 | 2 | 100% |
| 5 | Cattaneo, M. D., Jansson, M., and Nagasawa, K (2020) Bootstrap-based inference for cube root asymptotics | 0.737 | 5 | 4 | 40% |
| 6 | Prstgaard, J. and Wellner, J. A (1993) Exchangeably weighted bootstraps of the general empirical process | 0.737 | 4 | 3 | 50% |
| 7 | Liao, L., Gao, Y., and Kroer, C (2023) Statistical inference for fisher market equilibrium self | 0.737 | 4 | 2 | 75% |
| 8 | Hong, H. and Li, J (2020) The numerical bootstrap | 0.714 | 22 | 6 | 36% |
| 9 | Wellner, J. A. and Zhan, Y (1996) Bootstrapping z-estimators | 0.693 | 6 | 4 | 33% |
| 10 | Liao, H., Peng, L., Liu, Z., and Shen, X (2014) ipinyou global rtb bidding algorithm competition dataset | 0.644 | 4 | 2 | 50% |
Showing the top 10 of 74 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis | 0.000 | 1 | 1 |