arXiv 15 May 2023 · Econometrics
arXiv:2305.09052 · PDF · DOI · OpenAlex · Extracted main text
This study presents a novel approach to the density estimation of private values from second-price auctions, diverging from the conventional use of smoothing-based estimators. We introduce a Grenander-type estimator, constructed based on a shape restriction in the form of a convexity constraint. This constraint corresponds to the renowned Myerson regularity condition in auction theory, which is equivalent to the concavity of the revenue function for selling the auction item. Our estimator is nonparametric and does not require any tuning parameters. Under mild assumptions, we establish the cube-root consistency and show that the estimator asymptotically follows the scaled Chernoff's distribution. Moreover, we demonstrate that the estimator achieves the minimax optimal convergence rate.
appendix boundary found by appendix_command · 42% 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 | Ewerhart, C (2013) Regular type distributions in mechanism design and $-$concavity | 0.644 | 3 | 2 | 67% |
| 2 | Bulow, J. and P. Klemperer (1996) Auctions versus negotiations | 0.644 | 2 | 2 | 100% |
| 3 | Myerson, R. B (1981) Optimal auction design | 0.644 | 2 | 2 | 100% |
| 4 | Westling, T. and M. Carone (2020) A unified study of nonparametric inference for monotone functions | 0.511 | 5 | 2 | 20% |
| 5 | Luo, Y. and Y. Wan (2018) Integrated-quantile-based estimation for first-price auction models | 0.511 | 3 | 2 | 33% |
| 6 | Durot, C (2007) On the $L_p$-error of monotonicity constrained estimators | 0.511 | 2 | 2 | 50% |
| 7 | Groeneboom, P. and J. A. Wellner (2001) Computing chernoff's distribution | 0.511 | 2 | 1 | 100% |
| 8 | Henderson, D. J., J. A. List, D. L. Millimet, C. F. Parmeter, and M.… (2012) Empirical implementation of nonparametric first-price auction models | 0.405 | 1 | 1 | 100% |
| 9 | Szech, N (2011) Optimal advertising of auctions | 0.405 | 1 | 1 | 100% |
| 10 | Balabdaoui, F., H. Jankowski, M. Pavlides, A. Seregin, and J. Wellner (2011) On the grenander estimator at zero | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 30 scored citations.