Confidently Comparing Estimates with the c-value

References

• Balocchi, C., Deshpande, S. K., George, E. I., and Jensen, S. T. (2022), “Crime in Philadelphia: Bayesian Clustering with Particle Optimization,” Journal of the American Statistical Association, DOI: 10.1080/01621459.2022.2156348.
   Web of Science ®Google Scholar
• Balocchi, C., and Jensen, S. T. (2019), “Spatial Modeling of Trends in Crime Over Time in Philadelphia,” The Annals of Applied Statistics, 13, 2235–2259.
   Web of Science ®Google Scholar
• Bates, D., Mächler, M., Bolker, B., and Walker, S. (2015), “Fitting Linear Mixed-Effects Models using lme4,” Journal of Statistical Software, 67, 1–48.
   Web of Science ®Google Scholar
• Berk, R., Brown, L., Buja, A., Zhang, K., and Zhao, L. (2013), “Valid Post-Selection Inference,” The Annals of Statistics, 41, 802–837.
   Web of Science ®Google Scholar
• Berry, A. C. (1941), “The Accuracy of the Gaussian Approximation to the Sum of Independent Variates,” Transactions of the American Mathematical Society, 49, 122–136.
   Google Scholar
• Buka, S. L., Stichick, T. L., Birdthistle, I., and Earls, F. (2001), “Youth Exposure to Violence: Prevalance, Risks, and Consequences,” American Journal of Orthopsychiatry, 71, 298–310. DOI: 10.1037/0002-9432.71.3.298.
   PubMed Web of Science ®Google Scholar
• Casella, G., and Berger, R. L. (2002), Statistical Inference, Pacific Grove, CA: Duxbury.
   Google Scholar
• Claeskens, G., and Hjort, N. L. (2003), “The Focused Information Criterion,” Journal of the American Statistical Association, 98, 900–916.
   Web of Science ®Google Scholar
• Efron, B., and Morris, C. (1973), “Stein’s Estimation Rule and its Competitors — An Empirical Bayes Approach,” Journal of the American Statistical Association, 68, 117–130.
   Web of Science ®Google Scholar
• Fay, R. E., and Herriot, R. A. (1979), “Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data,” Journal of the American Statistical Association, 74, 269–277.
   Web of Science ®Google Scholar
• Hoff, P. D. (2021), “Smaller p-values via Indirect Information,” Journal of the American Statistical Association, 117, 1254–1269.
   Web of Science ®Google Scholar
• Kondo, M. C., Andreyeva, E., South, E. C., MacDonal, J. M., and Branas, C. C. (2018), “Neighborhood Interventions to Reduce Violence,” Annual Review of Public Health, 39, 253–271.
   PubMed Web of Science ®Google Scholar
• Lee, J. D., Sun, D. L., Sun, Y., and Taylor, J. E. (2016), “Exact Post-Selection Inference, with Application to the Lasso,” Annals of Statistics, 44, 907–927.
   Web of Science ®Google Scholar
• Lehmann, E. L., and Casella, G. (2006), Theory of Point Estimation, New York: Springer.
   Google Scholar
• Lindley, D. V., and Smith, A. F. (1972), “Bayes Estimates for the Linear Model,” Journal of the Royal Statistical Society, Series B, 34, 1–41.
   Google Scholar
• Lockhart, R., Taylor, J., Tibshirani, R. J., and Tibshirani, R. (2014), “A Significance Test for the Lasso,” Annals of Statistics, 42, 413–468. DOI: 10.1214/13-AOS1175.
   PubMed Web of Science ®Google Scholar
• Lodise, J., Özgökmen, T., Gonçalves, R. C., Iskandarani, M., Lund, B., Horstmann, J., Poulain, P.-M., Klymak, J., Ryan, E. H., and Guigand, C. (2020), “Investigating the Formation of Submesoscale Structures Along Mesoscale Fronts and Estimating Kinematic Quantities using Lagrangian Drifters,” Fluids, 5, 1–38.
   Web of Science ®Google Scholar
• Özgökmen, T. M. (2013), “GLAD Experiment CODE-style Drifter Trajectories (Low-Pass Filtered, 15 Minute Interval Records),” Northern Gulf of Mexico near DeSoto Canyon, July–October 2012. Harte Research Institute, Texas A&M University-Corpus Christi. Available at https://data.gulfresearchinitiative.org/data/R1.x134.073:0004
   Google Scholar
• Poje, A. C., Özgökmen, T. M., Lipphardt, B. L., Haus, B. K., Ryan, E. H., Haza, A. C., Jacobs, G. A., Reniers, A., Olascoaga, M. J., Novelli, G., Griffa, A., Beron-Vera, F. J., Chen, S. S., Coelho, E., Hogan, P. J., Kirwan, A. D. J., Huntley, H. S., and Mariano, A. J. (2014), “Submesoscale Dispersion in the Vicinity of the Deepwater Horizon Spill,” Proceedings of the National Academy of Sciences, 111, 12693–12698.
   PubMed Web of Science ®Google Scholar
• Rasmussen, C. E., and Williams, C. K. (2006), Gaussian Processes for Machine Learning, Cambridge, MA: MIT Press.
   Google Scholar
• Robbins, H. (1964), “The Empirical Bayes Approach to Statistical Decision Problems,” The Annals of Mathematical Statistics, 35, 1–20.
   Google Scholar
• Stein, C. M., (1981), “Estimation of the Mean of a Multivariate Normal Distribution,” The Annals of Statistics, 9, 1135–1151.
   Web of Science ®Google Scholar
• Taylor, J., and Tibshirani, R. (2018), “Post-Selection Inference for Penalized Likelihood Models,” Canadian Journal of Statistics, 46, 41–61.
   PubMed Web of Science ®Google Scholar
• Tian, X. (2020), “Prediction Error after Model Search,” Annals of Statistics, 48, 763–784.
   Web of Science ®Google Scholar
• Tibshirani, R., and Rosset, S. (2019), “Excess Optimism: How Biased is the Apparent Error of an Estimator Tuned by SURE?” Journal of the American Statistical Association, 114, 697–712.
   Web of Science ®Google Scholar
• Wallace, T. D. (1977), “Pretest Estimation in Regression: A Survey,” American Journal of Agricultural Economics, 59, 431–443.
   Web of Science ®Google Scholar