Abstract
This paper deals with the problem of how to adjust a predictive mean in a practical situation of prediction where there is asymmetry in the loss function. A standard linear model is considered for predicting the price of real estate using a normal-gamma conjugate prior for the parameters. The prior of a subject real estate agent is elicited but, for comparison, a diffuse prior is also considered. Three loss functions are used: asymmetric linear, asymmetric quadratic and LINEX, and the parameters under each of these postulated forms are elicited. Theoretical developments for prediction under each loss function in the presence of normal errors are presented and useful tables of adjustment factor values given. Predictions of the dependent price variable for two properties with differing characteristics are made under each loss function and the results compared.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Broemeling, L. D. (1985).Bayesian Analysis of Linear Models, Marcel Dekker, New York.
Cain, M. (1991). Minimal quantile measures of predictive cost with a generalized cost of error function, Economic Research Papers, No. 40, University of Wales, Aberystwyth.
Cain, M. and Owen, R. J. (1990). Regressor levels for Bayesian predictive response,J. Amer. Statist. Assoc.,85, 228–231.
Granger, C. W. J. (1969). Prediction with a generalized cost of error function,Operational Research Quarterly,20, 199–207.
Jeffreys, H. (1961).Theory of Probability, Clarendon Press, Oxford, U.K.
Savage, L. J. (1962).Bayesian Statistics: In Decision and Information Processes, Macmillan, New York.
Varian, H. R. (1975). A Bayesian approach to real estate assessment,Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage (eds. S. E. Fienberg and A. Zellner), 195–208, North-Holland, Amsterdam.
Wang, K., Grisson, T. V., Webb, J. R. and Spellman, L. (1991). The impact of rental properties on the value of single-family residences,Journal of Urban Economics,30, 152–166.
Zellner, A. (1971).An Introduction to Bayesian Inference in Econometrics, Wiley, New York.
Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss functions,J. Amer. Statist. Assoc.,81 (394), 446–451.
Zellner, A. and Chetty, V. K. (1965). Prediction and decision problems in regression models from the Bayesian point of view,J. Amer. Statist. Assoc.,60, 608–616.
Author information
Authors and Affiliations
About this article
Cite this article
Cain, M., Janssen, C. Real estate price prediction under asymmetric loss. Ann Inst Stat Math 47, 401–414 (1995). https://doi.org/10.1007/BF00773391
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00773391