Skip to main content
SpringerLink
Log in

Nonparametric methods with applications to hedonic models

  • Published:
The Journal of Real Estate Finance and Economics Aims and scope Submit manuscript

Abstract

Current real estate statistical valuation involves the estimation of parameters within a posited specification. Suchparametric estimation requires judgment concerning model (1) variables; and (2) functional form. In contrast,nonparametric regression estimation requires attention to (1) but permits greatly reduced attention to (2). Parametric estimators functionally model the parameters and variables affectingE(y¦x) while nonparametric estimators directly modelpdf(y, x) and henceE(y¦x).

This article applies the kernel nonparametric regression estimator to two different data sets and specifications. The article shows the nonparametric estimator outperforms the standard parametric estimator (OLS) across variable transformations and across data subsets differing in quality. In addition, the article reviews properties of nonparametric estimators, presents the history of nonparametric estimators in real estate, and discusses a representation of the kernel estimator as a nonparametric grid method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Azzalini, A., Bowman, A.W. and Hardle, W. “On the Use of Nonparametric Regression for Model Checking.”Biometrika 76 (1989), 1–11.

    Google Scholar 

  • Bellman, R.E.Adaptive Control Process. Princeton: Princeton University Press, 1961.

    Google Scholar 

  • Belsley, David. A., Kuh, Edwin and Welch, Roy E.Regression Diagnostics: Identifying Influential Data and Source of Collinearity. New York: John Wiley, 1980.

    Google Scholar 

  • Bierens, Herman J. “Kernel Estimators of Regression Functions.” In: T.F. Bewley, ed.,Advances in Econometrics-Fifth World Congress, Volume 1, Cambridge: Cambridge University Press, 1987, pp. 99–144.

    Google Scholar 

  • Box, G.E.P., and Cox, D.R. “An Analysis of Transformations.”Journal of the Royal Statistical Society, Series B 26 (1964), 211–243.

    Google Scholar 

  • Breiman, Leo “The II Method for Estimating Multivariate Functions from Noisy Data.”Technometrics 33 (1991), 125–160.

    Google Scholar 

  • Breiman, Leo, and Friedman, Jerome. “Estimating Optimal Transformations for Multiple Regression and Correlation.”Journal of the American Statistical Association 80 (1985), 580–619.

    Google Scholar 

  • Breiman, Leo, Friedman, Jerome, Olshen, R. and Stone, C.J.Classification and Regression Trees. Belmont, CA: Wadsworth Press, 1984.

    Google Scholar 

  • Broich, T., Hardle, W. and Krause, A.XploRe—a Computing Environment for eXploratory Regression, New York: Springer-Verlag, 1990.

    Google Scholar 

  • Buja, A., Hastie, T. and Tibshirani, R. “Linear Smoothers and Additive Models.”The Annals of Statistics 17 (1989), 453–555.

    Google Scholar 

  • Carroll, R.J., and Ruppert, D.Transformation and Weighting in Regression. New York: Chapman and Hall, 1988.

    Google Scholar 

  • Clapp, John, and Giaccotto, Carmelo. “Estimating Price Indices for Residential Property: A Comparison of Repeat Sales and Assessed Value Methods.”Journal of the American Statistical Association 87 (1992), 300–306.

    Google Scholar 

  • Cleveland, William S., and Devlin, Susan J. “Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting.”Journal of the American Statistical Association 83 (1988), 596–610.

    Google Scholar 

  • Colwell, Peter F., Cannaday, Roger E. and Wu, Chunchi. “The Analytical Foundations of Adjustment Grid Methods.”AREUEA Journal 11 (1983), 11–29.

    Google Scholar 

  • Delgado, Miguel A., and Stengos, Thanasis. “N-Kernel: A Review.”Journal of Applied Econometrics 5 (1990), 299–304.

    Google Scholar 

  • Duan, Naihua, and Li, Ker-Chau. “Slicing Regression: A Link-free Regression Method.”Annals of Statistics 19 (1991), 505–530.

    Google Scholar 

  • Efron, B.The Jacknife, the Bootstrap, and Other Resampling Plans. Philadelphia: Society for Applied Mathematics, 1982.

    Google Scholar 

  • Eubank, R.L., and Spiegelman, C.H. “Testing the Goodness of Fit of a Linear Model Via Nonparametric Regression Techniques.”Journal of the American Statistical Association 85 (1990), 387–392.

    Google Scholar 

  • Geisser, Seymour. “The Predictive Sample Reuse Method with Applications.”Journal of the American Statistical Association 70 (1975), 320–328.

    Google Scholar 

  • Friedman, Jerome. “Multivariate Adaptive Regression Splines.”Annals of Statistics 19 (1991), 1–141.

    Google Scholar 

  • Friedman, Jerome, and Stuetzle, W. “Projection Pursuit Regression.”Journal of the American Statistical Association 76 (1981), 817–823.

    Google Scholar 

  • Hall, Peter, and Jones, M.C. “Adaptive M-estimation in Nonparametric Regression.”Annals of Statistics 18 (190), 1712–1718.

  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A.Robust Statistics: The Approach Based on Influence Functions. New York: John Wiley, 1986.

    Google Scholar 

  • Hardle, Wolfgang.Applied Nonparametric Regression. Cambridge: Cambridge University Press, 1990.

    Google Scholar 

  • Hardle, Wolfgang, and Stoker, Thomas M. “Investigating Smooth Multiple Regression by the Method of Average Derivatives.”Journal of the American Statistical Association 84 (1989), 986–995.

    Google Scholar 

  • Harrison, David, and Rubinfeld, Daniel L. “Hedonic Housing Prices and the Demand for Clean Air.”Journal of Environmental Economics and Management 5 (1978), 81–102.

    Google Scholar 

  • Hartog, J., and Bierens, H.J. “Estimating a Hedonic Earnings Function with a Nonparametric Method.” In Aman Ullah, ed.,Semiparametric and Nonparametric Econometrics. Heidelberg: Physica-Verlag, 1989, pp. 145–171.

    Google Scholar 

  • Hong, Y., and Pagan, A. “Some Simulation Studies of Nonparametric Estimators.” In Aman Ullah, ed.,Semiparametric and Nonparametric Econometrics. Heidelberg: Physica-Verlag, 1989, pp. 129–144.

    Google Scholar 

  • Isakson, Hans R. “The Nearest Neighbors Appraisal Technique: An Alternative to the Adjustment Grid Methods.”AREUEA Journal 14 (1986), 274–286.

    Google Scholar 

  • Izenman, Alan J. “Recent Developments in Nonparameric Density Estimation.”Journal of the American Statistical Association 86 (1991), 205–224.

    Google Scholar 

  • Kang, Han-Bin, and Reichert, Alan K. “An Empirical Analysis of Hedonic Regression and Grid-Adjustment Techniques in Real Estate Appraisal.”AREUEA Journal 19 (1991), 70–91.

    Google Scholar 

  • Krasker, William S., Kuh, Edwin and Welsch, Roy E. “Estimation for Dirty Data and Flawed Models.” In Z. Griliches and M. Intriligator, eds.,Handbook of Econometrics, Volume 1, Amsterdam: North-Holland, 1983, pp. 651–98.

    Google Scholar 

  • Lipscomb, Joseph B., and Gray, J. Brian. “An Empirical Investigation of Four Market-Derived Adjustment Methods.”Journal of Real Estate Research 5 (1990), 53–66.

    Google Scholar 

  • Marron, J.S. “Automatic Smoothing Parameter Selection: A Survey.” In Aman Ullah, ed.,Semiparametric and Nonparametric Econometrics. Heidelberg: Physica-Verlag, 1989, pp. 65–86.

    Google Scholar 

  • McMillan, John, Ullah, Aman and Vinod, H.D. “Estimation of the Shape of the Demand Curve by Nonparametric Kernel Methods.” In B. Raj, ed.,Advances in Econometrics and Modelling. Dordrecht: Kluwer, 1989, pp. 85–92.

    Google Scholar 

  • Meese, Richard, and Wallace Nancy. “Nonparametric Estimation of Dynamic Hedonic Price Models and the Construction of Residential Housing Price Indices,”AREUEA Journal 19 (1991), 308–332.

    Google Scholar 

  • Messer, K. “A Comparison of a Spline Estimate to its Equivalent Kernel Estimate.”Annals of Statistics 19 (1991), 817–829.

    Google Scholar 

  • Moschini, Giancarlo, Prescott, David. M. and Stengos, Thanasis. “Nonparametric Kernel Estimation Applied to Forecasting: An Evaluation Based on the Bootstrap.” In Aman Ullah, ed.,Semiparametric and Nonparametric Econometrics. Heidelberg: Physica-Verlag, 1989, pp. 19–32.

    Google Scholar 

  • Nadaraya, E.A. “On Regression Estimators,”Theory of Probability and Applications 9 (1964), 157–159.

    Google Scholar 

  • Ng, Pin T., and Sickles, Robin C. “XploRe'-ing the World of Nonparametric Analysis.”Journal of Applied Econometrics 5 (1990), 293–298.

    Google Scholar 

  • Pindyck, R.S., and Rubinfeld, David L.Econometric Models and Economic Forecasts, 2nd ed., New York: McGraw-Hill, 1981.

    Google Scholar 

  • Powell, James L., Stock, James H. and Stoker, Thomas M. “Semiparametric Estimation of Index Coefficients.”Econometrica 57 (1989), 1403–1430.

    Google Scholar 

  • Robinson, P.M. “Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form.”Econometrica 55 (1987), 875–891.

    Google Scholar 

  • Robinson, P.M. “Semiparametric Econometrics: A Survey.”Journal of Applied Econometrics 3 (1988), 35–51.

    Google Scholar 

  • Rosenblatt, M. “Remarks on Some Nonparametric Estimates of Density Function.”Annals of Mathematical Statistics 27 (1956), 832–837.

    Google Scholar 

  • Singh, R.S., and Ullah, A. “Nonparametric Time Series Estimation of Joint DGP, Conditional DGP, and Vector Autocorrelation.”Econometric Theory 1 (1985), 27–52.

    Google Scholar 

  • Stone, M. “Cross-validatory Choice and Assessment of Statistical Prediction.”Journal of the Royal Statistical Society, Series B 36 (1974), 111–147.

    Google Scholar 

  • Subramanian, Shankar, and Carson, Richard T. “Robust Regression in the Presence of Heteroskedasticity.” In G.F. Rhodes and T.B. Fomby, eds.,Advances in Econometrics, Volume 7, Greenwich, Conn.: JAI Press, 1988, pp. 85–138.

    Google Scholar 

  • Sunderman, Mark, Birch, John, Cannaday, Roger and Hamilton, Thomas. “Testing for Vertical Inequity in Property Tax Systems.”Journal of Real Estate Research 5 (1990), 319–334.

    Google Scholar 

  • Titterington, D.M. “Common Structure of Smoothing Techniques in Statistics.”International Statistical Review 53 (1985), 141–170.

    Google Scholar 

  • Ullah, Aman. “Nonparametric Estimation of Economic Functionals.”Canadian Journal of Economics 21 (1988), 625–658.

    Google Scholar 

  • Watson, G.S. “Smooth Regression Analysis.”Sankhya, Series A 51 (1964), 175–186.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Management, University of Alaska, 99775, Fairbanks, Alaska

    R. Kelley Pace

Authors
  1. R. Kelley Pace
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pace, R.K. Nonparametric methods with applications to hedonic models. J Real Estate Finan Econ 7, 185–204 (1993). https://doi.org/10.1007/BF01096965

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01096965

Key words

Search

Navigation