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Exact computation of censored least absolute deviations estimator. (English) Zbl 07121292
Summary: We show that exact computation of the censored least absolute deviations (CLAD) estimator proposed by J. L. Powell [J. Econom. 25, 303–325 (1984; Zbl 0571.62100)] may be achieved by formulating the estimator as a linear Mixed Integer Programming (MIP) problem with disjunctive constraints. We apply our approach to three previously studied datasets and find that widely used approximate optimization algorithms can lead to erroneous conclusions. Extensive simulations confirm that MIP-based computation using available solvers is effective for datasets typically encountered in econometric applications and that, despite the proliferation of competitors, CLAD remains a useful estimator.
MSC:
62 Statistics
91 Game theory, economics, finance, and other social and behavioral sciences
Software:
NMOF; quantreg; SCIP
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[1] Achterberg, T., SCIP: solving constraint integer programs, Math. Program. Comput., 1, 1, 1-41, (2009) · Zbl 1171.90476
[2] Andrews, D., A stopping rule for the computation of generalized method of moments estimators, Econometrica, 65, 4, 913-931, (1997) · Zbl 0899.62101
[3] Barrodale, I.; Roberts, F. D.K., An improved algorithm for discrete \(L_1\) linear approximation, SIAM J. Numer. Anal., 10, 5, 839-848, (1973) · Zbl 0266.65016
[4] Bilias, Y.; Chen, S.; Ying, Z., Simple resampling methods for censored regression quantiles, J. Econometrics, 99, 2, 373-386, (2000) · Zbl 1076.62567
[5] Buchinsky, M., Changes in the U.S. wage structure 1963-1987: Application of quantile regression, Econometrica, 62, 2, 405-458, (1994) · Zbl 0800.90235
[6] Buchinsky, M.; Hahn, J., An alternative estimator for the censored quantile regression model, Econometrica, 66, 3, 653-671, (1998) · Zbl 1055.62569
[7] Chen, S., Sequential estimation of censored quantile regression models, J. Econometrics, 207, 1, 30-52, (2018) · Zbl 06952481
[8] Chen, L.-Y.; Lee, S., Best subset binary prediction, J. Econometrics, 206, 1, 39-56, (2018) · Zbl 1398.62362
[9] Chernozhukov, V.; Hong, H., Three-step censored quantile regression and extramarital affairs, J. Amer. Statist. Assoc., 97, 459, 872-882, (2002) · Zbl 1048.62112
[10] Chernozhukov, V.; Hong, H., An MCMC approach to classical estimation, J. Econometrics, 115, 2, 293-346, (2003) · Zbl 1043.62022
[11] Fafchamps, M.; Gunning, J. W.; Oostendorp, R., Inventories and risk in African manufacturing, Econ. J., 110, 466, 861-893, (2000)
[12] Fair, R. C., A theory of extramarital affairs, J. Political Econ., 86, 1, 45-61, (1978)
[13] Fitzenberger, B., A Note on Estimating Censored Quantile Regressions, (1994), Discussion Paper, Center for International Labor Economics (CILE), University of Konstanz, Technical Report · Zbl 0908.62031
[14] Fitzenberger, B., A guide to censored quantile regressions, (Maddala, G. S.; Rao, C. R., Robust Inference, Handbook of Statistics, Vol. 15, (1997), North-Holland: North-Holland Amsterdam), 405-437 · Zbl 0908.62031
[15] Fitzenberger, B., Computational aspects of censored quantile regression, (Dodge, Y., Proceedings of the 3rd International Conference on Statistical Data Analysis Based on the L1-Norm and Related Methods, Vol. 31, (1997), IMS Lecture Notes Series: IMS Lecture Notes Series Hayword, CA), 171-186 · Zbl 0933.62058
[16] Fitzenberger, B.; Winker, P., Improving the computation of censored quantile regressions, Comput. Statist. Data Anal., 52, 1, 88-108, (2007) · Zbl 05560142
[17] Florios, K.; Skouras, S., Exact computation of max weighted score estimators, J. Econometrics, 146, 1, 86-91, (2008) · Zbl 1418.62450
[18] Floudas, C. A., Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications, (1995), Oxford University Press · Zbl 0886.90106
[19] Khan, S.; Powell, J., Two-step estimation of semiparametric censored regression models, J. Econometrics, 103, 1-2, 73-110, (2001) · Zbl 1053.62050
[20] Kitagawa, T.; Tetenov, A., Who should be treated? Empirical welfare maximization methods for treatment choice, Econometrica, 86, 2, 591-616, (2018) · Zbl 1419.91280
[21] Koenker, R., Censored quantile regression redux, J. Stat. Softw., 27, 6, 1-25, (2008)
[22] Koenker, R., quantreg: Quantile Regression, (2012), R package version 4.79
[23] Koenker, R.; Park, B. J., An interior point algorithm for nonlinear quantile regression, J. Econometrics, 71, 1-2, 265-283, (1996) · Zbl 0855.62030
[24] Lin, G.; He, X.; Portnoy, S., Quantile regression with doubly censored data, Comput. Statist. Data Anal., 56, 4, 797-812, (2012) · Zbl 1243.62056
[25] Manski, C., Maximum score estimation of the stochastic utility model of choice, J. Econometrics, 3, 3, 205-228, (1975) · Zbl 0307.62068
[26] Nemhauser, G. L.; Wolsey, L. A., Integer and Combinatorial Optimization, (1999), Wiley · Zbl 0944.90001
[27] Papadimitriou, C. H.; Steiglitz, K., Combinatorial Optimization: Algorithms and Complexity, (1998), Dover · Zbl 0944.90066
[28] Peng, L.; Huang, Y., Survival analysis with quantile regression models, J. Amer. Statist. Assoc., 103, 482, 637-649, (2008) · Zbl 1408.62159
[29] Portnoy, S., Censored regression quantiles, J. Amer. Statist. Assoc., 98, 464, 1001-1012, (2003) · Zbl 1045.62099
[30] Portnoy, S., Is ignorance bliss: Fixed vs. random censoring, (Antoch, J.; Huskova, M.; Sen, P. K., Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in Honor of Professor Jana Jureckova, Vol. 7, (2010), IMS), 215-223
[31] Powell, J., Least absolute deviations estimation for the censored regression model, J. Econometrics, 25, 3, 303-325, (1984) · Zbl 0571.62100
[32] Powell, J., Censored regression quantiles, J. Econometrics, 32, 1, 143-155, (1986) · Zbl 0605.62139
[33] Schumann, E., NMOF: Numerical Methods and Optimization in Finance, (2017), R package version 1.1-0
[34] Tang, Y.; Wang, H.; He, X.; Zhu, Z., An informative subset-based estimator for censored quantile regression, Test, 21, 4, 635-655, (2012) · Zbl 1284.62269
[35] Womersley, R. S., Censored discrete linear l1 approximation, SIAM J. Sci. Stat. Comput., 7, 1, 105-122, (1986) · Zbl 0617.90076
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