Volume 2013 (2013), Article ID 158240, 16 pages
Choosing the Right Spatial Weighting Matrix in a Quantile Regression Model
Lancashire Business School, University of Central Lancashire, Greenbank Building, Preston,
Lancashire PR1 2HE, UK
Received 4 December 2012; Accepted 27 December 2012
Academic Editors: D. M. Hanink and W. R. Reed
Copyright © 2013 Philip Kostov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- P. Kostov, “A spatial quantile regression hedonic model of agricultural land prices,” Spatial Economic Analysis, vol. 4, no. 1, pp. 53–72, 2009.
- F. Stetzer, “Specifying weights in spatial forecasting models: the results of some experiments,” Environment & Planning A, vol. 14, no. 5, pp. 571–584, 1982.
- L. Anselin, “Under the hood issues in the specification and interpretation of spatial regression models,” Agricultural Economics, vol. 27, no. 3, pp. 247–267, 2002.
- B. Fingleton, “Externalities, economic geography, and spatial econometrics: conceptual and modeling developments,” International Regional Science Review, vol. 26, no. 2, pp. 197–207, 2003.
- G. Holloway and M. L. A. Lapar, “How big is your neighbourhood? Spatial implications of market participation among filipino smallholders,” Journal of Agricultural Economics, vol. 58, no. 1, pp. 37–60, 2007.
- J. P. LeSage and O. Parent, “Bayesian model averaging for spatial econometric models,” Geographical Analysis, vol. 39, no. 3, pp. 241–267, 2007.
- J. P. LeSage and M. M. Fischer, “Spatial growth regressions: model specification, estimation and interpretation,” Spatial Economic Analysis, vol. 3, no. 3, pp. 275–304, 2008.
- J. Crespo-Cuaresma and M. Feldkircher, “Spatial filtering, model uncertainty and the speed of income convergence in Europe,” in Annual Meeting of the Austrian Economic Association, 2010, http://www.univie.ac.at/economics/noeg2010/papers/Crespo_Cuaresma_NOEG2010.pdf.
- T. S. Eicher, A. Lenkoski, and A. E. Raftery, “Bayesian model averaging and endogeneity under model uncertainty: an application to development determinants,” UW Working Paper UWEC-2009-19, University of Washington, Department of Economics, 2009.
- P. Kostov, “Model boosting for spatial weighting matrix selection in spatial lag models,” Environment and Planning B, vol. 37, no. 3, pp. 533–549, 2010.
- H. H. Kelejian and I. R. Prucha, “A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances,” Journal of Real Estate Finance and Economics, vol. 17, no. 1, pp. 99–121, 1998.
- J. Zietz, E. N. Zietz, and G. S. Sirmans, “Determinants of house prices: a quantile regression approach,” Journal of Real Estate Finance and Economics, vol. 37, no. 4, pp. 317–333, 2008.
- T. H. Kim and C. Muller, “Two-stage quantile regression when the first stage is based on quantile regression,” Econometrics Journal, vol. 7, pp. 218–231, 2004.
- V. Chernozhukov and C. Hansen, “Instrumental quantile regression inference for structural and treatment effect models,” Journal of Econometrics, vol. 132, no. 2, pp. 491–525, 2006.
- V. Chernozhukov and C. Hansen, “Instrumental variable quantile regression: a robust inference approach,” Journal of Econometrics, vol. 142, no. 1, pp. 379–398, 2008.
- V. Chernozhukov and H. Hong, “An MCMC approach to classical estimation,” Journal of Econometrics, vol. 115, no. 2, pp. 293–346, 2003.
- O. Arias, K. F. Hallock, and W. Sosa-Escudero, “Individual heterogeneity in the returns to schooling: instrumental variables quantile regression using twins data,” Empirical Economics, vol. 26, no. 1, pp. 7–40, 2001.
- J. García, P. J. Hernández, and A. López-Nicolás, “How wide is the gap? An investigation of gender wage differences using quantile regression,” Empirical Economics, vol. 26, no. 1, pp. 149–167, 2001.
- N. Fenske, T. Kneib, and T. Hothorn, “Identifying risk factors for severe childhood malnutrition by boosting additive quantile regression,” Technical Report No. 52, Department of Statistics, LMU München, 2009.
- R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society B, vol. 58, pp. 267–288, 1996.
- J. Fan and R. Li, “Variable selection via nonconcave penalized likelihood and its oracle properties,” Journal of the American Statistical Association, vol. 96, no. 456, pp. 1348–1360, 2001.
- Y. Li and J. Zhu, “L1-norm quantile regression,” Journal of Computational and Graphical Statistics, vol. 17, no. 1, pp. 163–185, 2008.
- Y. Wu and Y. Liu, “Variable selection in quantile regression,” Statistica Sinica, vol. 19, no. 2, pp. 801–817, 2009.
- A. Belloni and V. Chernozhukov, “L1-penalized quantile regression in high-dimensional sparse models,” WP10/09, Centre For Microdata Methods and Practice, Institute for Fiscal Studies, 2009.
- E. Greenshtein and Y. Ritov, “Persistence in high-dimensional linear predictor selection and the virtue of overparametrization,” Bernoulli, vol. 10, no. 6, pp. 971–988, 2004.
- J. Fan and J. Lv, “Sure independence screening for ultrahigh dimensional feature space,” Journal of the Royal Statistical Society B, vol. 70, no. 5, pp. 849–911, 2008.
- L. Wasserman and K. Roeder, “High-dimensional variable selection,” Annals of Statistics A, vol. 37, no. 5, pp. 2178–2201, 2009.
- N. Meinshausen and P. Bühlmann, “Stability selection,” Journal of the Royal Statistical Society B, vol. 72, no. 4, pp. 417–473, 2010.
- R. Koenker and G. Bassett, “Regression quantiles,” Econometrica, vol. 46, pp. 33–50, 1978.
- H. Zou and M. Yuan, “Regularized simultaneous model selection in multiple quantiles regression,” Computational Statistics and Data Analysis, vol. 52, no. 12, pp. 5296–5304, 2008.
- H. Zou and T. Hastie, “Regularization and variable selection via the elastic net,” Journal of the Royal Statistical Society B, vol. 67, no. 2, pp. 301–320, 2005.
- H. Wang and C. Leng, “Unified LASSO estimation by least squares approximation,” Journal of the American Statistical Association, vol. 102, no. 479, pp. 1039–1048, 2007.
- B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” Annals of Statistics, vol. 32, no. 2, pp. 407–499, 2004.
- H. Wang, R. Li, and C. L. Tsai, “Regression coefficient and autoregressive order shrinkage and selection via the lasso,” Journal of the Royal Statistical Society B, vol. 69, no. 1, pp. 63–78, 2007.
- W. K. Newey and J. L. Powell, “Efficient estimation of linear and type I censored regression models under conditional quantile restrictions,” Econometric Theory, vol. 6, pp. 295–317, 1990.
- D. Harrison and D. L. Rubinfeld, “Hedonic Housing Prices and the Demand for Clean Air,” Journal of Environmental Economics and Management, vol. 5, pp. 81–102, 1978.
- O.W. Gilley and R. K. Pace, “On the Harrison and Rubinfeld Data,” Journal of Environmental Economics and Management, vol. 3, pp. 403–405, 1996.
- H. Wang, “Factor profiling for ultra high dimensional variable selection,” Working Paper, 2011, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1613452.
- H. Cho and P. Fryzlewicz, “High-dimensional variable selection via tilting,” 2010, High-dimensional variable selection, http://stats.lse.ac.uk/fryzlewicz/tilt/tilt.pdf.
- R: Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2009, http://www.R-project.org.