Spatial Quantile Regression

Grażyna Trzpiot

doi:10.2478/v10103-012-0040-8

Authors

Grażyna Trzpiot University of Economics in Katowice

DOI:

https://doi.org/10.2478/v10103-012-0040-8

Abstract

In a number of applications, a crucial problem consists in describing and analyzing the influence of a vector Xi of covariates on some real-valued response variable Yi. In the present context, where the observations are made over a collection of sites, this study is more difficult, due to the complexity of the possible spatial dependence among the various sites. In this paper, instead of spatial mean regression, we thus consider the spatial quantile regression functions. Quantile regression has been considered in a spatial context. The main aim of this paper is to incorporate quantile regression and spatial econometric modeling. Substantial variation exists across quantiles, suggesting that ordinary regression is insufficient on its own. Quantile estimates of a spatial-lag model show considerable spatial dependence in the different parts of the distribution.

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References

Buchinsky M. (1998), Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research, Journal of Human Resources, 33
Google Scholar

Chambers R., Pratesi M., Salvati N., Tzavidis N. (2005), Small Area Estimation: spatial information and M- quantile regression to estimate the average production of olive per farm, Wp 279, Dipatimento di Statistica e Matematica Applicata all’Economia, Universita di Pisa
Google Scholar

Chernozhukov V., Hansen Ch.. (2006), Instrumental Quantile Regression Inference for Structural and Treatment Effect Models, Journal of Econometrics, 132
Google Scholar

Cleveland, W. S. (1994), Coplots, Nonparametric Regression, and Conditionally Parametric Fits. In T.W. Anderson, K.T. Fant, and I. Olkin (Eds.), Multivariate Analysis and its Applications, Hayward: Institute of Mathematical Statistics.
Google Scholar

Kim T.-H., Muller Ch.. (2004), Two-Stage Quantile Regression when the First Stage is Based on Quantile Regression, Econometrics Journal, 7
Google Scholar

Koenker R., Basset B., (1978), Regression Quantiles, Econometrica, Vol 46
Google Scholar

Koenker R., Ng P., (2005), Inequality Constrained Quantile Regression, The Indian Journal of Statistics, Vol. 67
Google Scholar

Koenker R., Hallock K. F. (2001), Quantile Regression, Journal of Economic Perspectives, 15
Google Scholar

Koenker R., Mizera I. (2004). Penalized Triograms: Total Variation Regularization for Bivariate Smoothing, Journal of the Royal Statistical Society: Series B, 66
Google Scholar

Kostov, P. (2009), A Spatial Quantile Regression Hedonic Model of Agricultural Land Prices, Spatial Economic Analysis, 4
Google Scholar

Liao, Wen-Chi and Xizhu Wang (2012), “Hedonic House Prices and Spatial Quantile Regression,” Journal of Housing Economics, 21, 16-27
Google Scholar

Mcmillan. D. P. (2010), Issues in Spatial Data Analysis, Journal of Regional Science, 119-141.
Google Scholar

Trzpiot G., (2008), The Implementation of Quantile Regression Methodology in VaR Estimation “Studies and Researches of Faculty of Economics and Management University of Szczecin”,
Google Scholar

Trzpiot G., (2009 a), Quantile Regression Model versus Factor Model Estimation, in: Financial Investments and Insurances”, University of Economics in Wrocław, Vol 60
Google Scholar

Trzpiot G., (2009 b), Application weighted VaR in capital allocation, Polish Journal of Environmental Studies, Olsztyn, Vol 18, 5B
Google Scholar

Trzpiot G., (2009 c), Estimation methods for quantile regression, Economics Studies 53, Karol Adamiecki University of Economics in Katowice
Google Scholar

Trzpiot G., (2010), Quantile Regression Model of Return Rate Relation – Volatility for Some Warsaw Stock Exchange Indexes, (in Polish), Finances, Financial Markets and Insurances. Capital Market, University of Szczecin, Vol 28, 61-76
Google Scholar

Trzpiot G. (2011a). Bayesian Quantile Regression, Studia Ekonomiczne, Zeszyty Naukowe nr 65, Uniwersytet Ekonomiczny w Katowicach, 33-44
Google Scholar

Trzpiot G. (2011b). Some tests for quantile regression models, Acta Universitatis Lodziensis, Łódź, Folia Economica, 255, 125-135
Google Scholar

Zeitz J., Zietz E. N., Sirmans G. S. (2008) Determinants of House Prices: A Quantile Regression Approach, Journal of Real Estate Finance and Economics, 37
Google Scholar