Confidence intervals for intentionally biased estimators

References

• Angrist, J., Chernozhukov, V., Fernandez-Val, I. ( 2006). Quantile regression under misspecification, with an application to the U.S. Wage structure. Econometrica 74(2):539–563. doi:10.1111/j.1468-0262.2006.00671.x.
   Web of Science ®Google Scholar
• Armstrong, T. B., Kline, P., Sun, L. ( 2023). Adapting to misspecification, Working paper available at, https://arxiv.org/abs/2305.14265.
   Google Scholar
• Armstrong, T. B., Kolesár, M. ( 2020). Simple and honest confidence intervals in nonparametric regression. Quantitative Economics 11(1):1–39. doi:10.3982/QE1199.
   Web of Science ®Google Scholar
• Armstrong, T. B., Kolesár, M. ( 2021). Sensitivity analysis using approximate moment condition models. Quantitative Economics, 12(1):77–108. doi:10.3982/QE1609.
   Web of Science ®Google Scholar
• Chen, L., Lee, S. ( 2018). Exact computation of GMM estimators for instrumental variable quantile regression models. Journal of Applied Econometrics 33(4):553–567. doi:10.1002/jae.2619.
   Web of Science ®Google Scholar
• Cheng, XU., Liao, Z., Shi, R. ( 2019). On uniform asymptotic risk of averaging GMM estimators. Quantitative Economics 10(3):931–979. doi:10.3982/QE711.
   Web of Science ®Google Scholar
• Chernozhukov, V., Hansen, C. ( 2005). An IV model of quantile treatment effects. Econometrica 73(1):245–261. doi:10.1111/j.1468-0262.2005.00570.x.
   Web of Science ®Google Scholar
• Chernozhukov, V., Hansen, C. ( 2006). Instrumental quantile regression inference for structural and treatment effect models. Journal of Econometrics, 132(2):491–525. doi:10.1016/j.jeconom.2005.02.009.
   Web of Science ®Google Scholar
• Chetverikov, D., Liao, Z., Chernozhukov, V. ( 2021). On cross-validated lasso in high dimensions. Annals of Statistics, 49(3):1300–1317. doi:10.1214/20-AOS2000.
   Web of Science ®Google Scholar
• DiTraglia, F. J. ( 2016). Using invalid instruments on purpose: Focused moment selection and averaging for GMM. Journal of Econometrics 195(2):187–208. doi:10.1016/j.jeconom.2016.07.006
   Web of Science ®Google Scholar
• Donoho, D. L. ( 1994). Statistical estimation and optimal recovery. Annals of Statistics, 22(1):238–270. doi:10.1214/aos/1176325367.
   Web of Science ®Google Scholar
• Fan, J., Li, R. ( 2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96(456):1348–1360. doi:10.1198/016214501753382273
   Web of Science ®Google Scholar
• Fernandes, M., Guerre, E., Horta, E. ( 2021). Smoothing quantile regressions. Journal of Business & Economic Statistics 39(1):338–357. doi:10.1080/07350015.2019.1660177
   Web of Science ®Google Scholar
• Groeneboom, P., Jongbloed, G., Witte, B. I. ( 2010). Maximum smoothed likelihood estimation and smoothed maximum likelihood estimation in the current status model. Annals of Statistics, 38(1):352–387. doi:10.1214/09-AOS721.
   Web of Science ®Google Scholar
• Groeneboom, P., Wellner, J. A. ( 1992). Information Bounds and Nonparametric Maximum Likelihood Estimation. Basel, Switzerland: Birkhäuser.
   Google Scholar
• Hansen, B. E. ( 2017). Stein-LIKE 2SLS estimator. Econometric Reviews 36(6–9):840–852. doi:10.1080/07474938.2017.1307579.
   Web of Science ®Google Scholar
• He, X., Pan, X., Tan, K. M., Zhou, W.-X. ( 2023). Smoothed quantile regression with large-scale inference. Journal of Econometrics 232(2):367–388. doi:10.1016/j.jeconom.2021.07.01036776480.
   PubMed Web of Science ®Google Scholar
• Hoerl, A. E., Kennard, R. W. ( 1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12(1):55–67. doi:10.1080/00401706.1970.10488634
   Web of Science ®Google Scholar
• Horowitz, J. L. ( 1992). A smoothed maximum score estimator for the binary response model. Econometrica 60(3):505. doi:10.2307/2951582.
   Web of Science ®Google Scholar
• James, W., C., Stein , (1961). Estimation with quadratic loss. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, Berkeley, CA: University of California Press, 361–379. https://projecteuclid.org/euclid.bsmsp/1200512173.
   Google Scholar
• Kaido, H., Wüthrich, K. ( 2021). Decentralization estimators for instrumental variable quantile regression models. Quantitative Economics 12(2):443–475. doi:10.3982/QE1440.
   Web of Science ®Google Scholar
• Kaplan, D. M. ( 2022). Smoothed instrumental variables quantile regression. The Stata Journal: Promoting Communications on Statistics and Stata 22(2):379–403. doi:10.1177/1536867X221106404.
   Google Scholar
• Kaplan, D. M., Sun, Y. ( 2017). Smoothed estimating equations for instrumental variables quantile regression. Econometric Theory 33(1):105–157. doi:10.1017/S0266466615000407.
   Web of Science ®Google Scholar
• Knight, K., Fu, W. ( 2000). Asymptotics for lasso-type estimators. Annals of Statistics, 28(5):1356–1378. https://www.jstor.org/stable/2674097.
   Web of Science ®Google Scholar
• Koenker, R., ( 2023). quantreg: Quantile Regression. Available at: https://CRAN.R-project.org/package=quantreg.Rpackageversion5.96.
   Google Scholar
• Koenker, R., Bassett, G. ( 1978). Regression quantiles. Econometrica 46(1):33 doi:10.2307/1913643.
   Web of Science ®Google Scholar
• Leeb, H., Pötscher, B. M. ( 2008). Sparse estimators and the oracle property, or the return of hodges’ estimator. Journal of Econometrics 142(1):201–211. doi:10.1016/j.jeconom.2007.05.017.
   Web of Science ®Google Scholar
• Liu, C.-A. ( 2015). Distribution theory of the least squares averaging estimator. Journal of Econometrics 186(1):142–159. doi:10.1016/j.jeconom.2014.07.002.
   Web of Science ®Google Scholar
• Liu, X. ( 2022). Averaging estimation for instrumental variables quantile regression, Working paper. Available at: https://xinliu16.github.io/.
   Google Scholar
• Maasoumi, E. ( 1978). A modified stein-LIKE estimator for the reduced form coefficients of simultaneous equations. Econometrica 46(3):695. doi:10.2307/1914241.
   Web of Science ®Google Scholar
• Manski, C. F. ( 1975). Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics, 3(3):90032–90041. doi:10.1016/0304-4076(75).
   Google Scholar
• Politis, D. N., Romano, J. P. ( 1994). Large sample confidence regions based on subsamples under minimal assumptions. Annals of Statistics, 22(4):2031–2050.
   Web of Science ®Google Scholar
• R Core Team ( 2023). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org.
   Google Scholar
• Stein, C. M. ( 1962). Confidence sets for the mean of a multivariate normal distribution. Journal of the Royal Statistical Society: Series B (Methodological) 24(2):265–285. doi:10.1111/j.2517-6161.1962.tb00458.x.
   Google Scholar
• Tibshirani, R. ( 1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58(1):267–288. doi:10.1111/j.2517-6161.1996.tb02080.x.
   Web of Science ®Google Scholar
• Zou, H. ( 2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101(476):1418–1429. doi:10.1198/016214506000000735.
   Web of Science ®Google Scholar