Kontek, Krzysztof (2010): Density Based Regression for Inhomogeneous Data: Application to Lottery Experiments.

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Abstract
This paper presents a regression procedure for inhomogeneous data characterized by varying variance, skewness and kurtosis or by an unequal amount of data over the estimation domain. The concept is based first on the estimation of the densities of an observed variable for given values of explanatory variable(s). These density functions are then used to estimate the relation between all the variables. The mean, quantile (including median) and mode regression estimators are proposed, with the last one appearing to be the maximum likelihood estimator in the density based approach. The paper demonstrates the advantages of the proposed methodology, which eliminates most of the estimation problems arising from data inhomogeneity. These include the computational inconveniences of the standard quantile and mode regression techniques. The proposed methodology, when applied to lottery experiments, makes it possible to confirm and to extend the previously presented conclusion (Kontek, 2010) that lottery valuations are only nonlinear with respect to probability when medians and means are considered. Such nonlinearity disappears once modes are considered. This means that the most likely behavior of a group is fully rational. The regression procedure presented in this paper is, however, very general and may be applied in many other cases of data inhomogeneity and not just lottery experiments.
Item Type:  MPRA Paper 

Original Title:  Density Based Regression for Inhomogeneous Data: Application to Lottery Experiments 
Language:  English 
Keywords:  Density Distribution; Least Squares, Quantile, Median, Mode, Maximum Likelihood Estimators; Lottery experiments; Relative Utility Function; Prospect Theory. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C16  Specific Distributions C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions; Specific Statistics C  Mathematical and Quantitative Methods > C9  Design of Experiments > C91  Laboratory, Individual Behavior D  Microeconomics > D0  General > D03  Behavioral Economics; Underlying Principles C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology; Computer Programs > C81  Methodology for Collecting, Estimating, and Organizing Microeconomic Data C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C21  CrossSectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D87  Neuroeconomics 
Item ID:  22268 
Depositing User:  Krzysztof Kontek 
Date Deposited:  21. Apr 2010 21:56 
Last Modified:  19. Feb 2013 12:33 
References:  1. Cameron, A. C., Trivedi, P. K., (2005). Microeconometrics. Methods and Applications, Cambridge University Press. 2. Gupta, A. K., Nadarajah, S., (2004), Handbook of Beta Distribution and Its Applications, Marcel Dekker, Inc, New York. 3. Idzikowska, K., (2009). Determinants of the probability weighting function, presented under name Katarzyna Domurat at SPUSM22 Conference, Rovereto, Italy, August 2009, paper Id = 182, http://discof.unitn.it/spudm22/program_24.jsp . 4. Kontek, K., (2010). Mean, median or Mode? A Striking Conclusion from Lottery Experiments, MPRA Paper http://mpra.ub.unimuenchen.de/21758/, Available at SSRN: http://ssrn.com/abstract=1581436 5. Kontek, K., (2009). Lottery Valuation Using the Aspiration / Relative Utility Function, Warsaw School of Economics, Department of Applied Econometrics Working Paper no. 39. Available at SSRN: http://ssrn.com/abstract=1437420 and RePec:wse:wpaper:39. 6. Libby, D. L., Novick, M. R., (1982). Multivariate generalized beta distributions with applications to utility assessment, Journal of Educational Statistics, 7, pp 271294. 7. Traub, S., Schmidt, U., (2009). An Experimental Investigation of the Disparity between WTA and WTP for Lotteries, Theory & Decision 66 (2009), pp 229262. 8. Tversky A., Kahneman D., (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty, Journal of Risk and Uncertainty, vol. 5(4), October, pp 297323. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/22268 