Density Based Regression for Inhomogeneous Data: Application to Lottery Experiments
AbstractThis 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 re-gression 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 pro-posed 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 22268.
Date of creation: 21 Apr 2010
Date of revision:
Density Distribution; Least Squares; Quantile; Median; Mode; Maximum Likelihood Estimators; Lottery experiments; Relative Utility Function; Prospect Theory.;
Find related papers by JEL classification:
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
- D03 - Microeconomics - - General - - - Behavioral Microeconomics; Underlying Principles
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- C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-02 (All new papers)
- NEP-ECM-2010-05-02 (Econometrics)
- NEP-UPT-2010-05-02 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
- Krzysztof Kontek, 2009. "Lottery valuation using the aspiration / relative utility function," Working Papers 39, Department of Applied Econometrics, Warsaw School of Economics.
- Kontek, Krzysztof, 2010. "Mean, Median or Mode? A Striking Conclusion From Lottery Experiments," MPRA Paper 21758, University Library of Munich, Germany.
- Schmidt, Ulrich & Traub, Stefan, 2009.
"An experimental investigation of the disparity between WTA and WTP for lotteries,"
Open Access Publications from Kiel Institute for the World Economy
28786, Kiel Institute for the World Economy (IfW).
- Ulrich Schmidt & Stefan Traub, 2009. "An Experimental Investigation of the Disparity Between WTA and WTP for Lotteries," Theory and Decision, Springer, vol. 66(3), pages 229-262, March.
- Traub, Stefan & Schmidt, Ulrich, 2006. "An Experimental Investigation of the Disparity between WTA and WTP for Lotteries," Economics Working Papers 2006,09, Christian-Albrechts-University of Kiel, Department of Economics.
- Kontek, Krzysztof, 2010. "Estimation of Peaked Densities Over the Interval [0,1] Using Two-Sided Power Distribution: Application to Lottery Experiments," MPRA Paper 22378, University Library of Munich, Germany.
- Kontek, Krzysztof, 2010. "Multi-Outcome Lotteries: Prospect Theory vs. Relative Utility," MPRA Paper 22947, University Library of Munich, Germany.
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