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Comparing market areas using kernel density estimation

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Abstract

From a managers’ point of view it is useful to know whether or not a market area has changed over time, and whether two market areas are different. In this paper we propose, using the kernel density estimation method, to estimate the density of a market area and show how the estimated market area densities may be compared for differences using Bayesian cross-validated likelihood methods. The proposed methodology is highlighted using two applications. One application involves comparison of lunch and dinner markets of a restaurant and the other application involves identifying the optimal area for a direct mail program.

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References

  • Akaike, H. 1973. “Information Theory and an Extension of the Maximum Likelihood Principle.” InProceedings of the 2nd International Symposium of Information Theory, pp. 267–281. Eds. N. Petrov and F. Csadki. Budapest: Akademiai Kiado.

    Google Scholar 

  • Akaike, H. 1974. “A New Look at the Statistical Model Identification.”IEEE Transactions in Automatic Control 19: 716–723.

    Article  Google Scholar 

  • Atkinson, A. C. 1969. “A Model for Discriminating Between Models.”Journal of Royal Statistical Society 32 (B): 323–353.

    Google Scholar 

  • Blattberg, Robert C. and Subrata K. Sen. 1973. “An Evaluation of the Application of Minimum Chi-Square Procedures of Stochastic Models of Brand Choice.”Journal of Marketing Research 10: 421–427.

    Article  Google Scholar 

  • Donthu, Naveen and Roland T. Rust. 1989. “Estimating Geographic Consumer Density Using Kernel Density Estimation.”Marketing Science 8: 191–203.

    Google Scholar 

  • Epanechnikov, V. A. 1969. “Nonparametric Estimation of a Multivariate Probability Density.”Theory of Probability and Applications 14: 153–158.

    Article  Google Scholar 

  • Fornell, Claes and Roland T. Rust. 1989. “Incorporating Prior Theory in Covariance Model Comparison: Application of Bayesian Methods.”Psychometrika, forthcoming.

  • Fryer, M. J. 1977. “A Review of Some Non-Parametric Methods of Density Estimation.”Journal of Institute of Mathematical Applications 18: 371–380.

    Article  Google Scholar 

  • Hauser, John R. 1978. “Testing the Accuracy, Usefulness, and Significance of Probabilistic Choice Models: An Information Theoretic Approach.”Operations Research 26: 406–421.

    Google Scholar 

  • Huff, David L. and Richard R. Batsell. 1977. “Delimiting the Areal Extent of a Market Area.”Journal of Marketing Research 14: 581–585.

    Article  Google Scholar 

  • Huff, David L. and Roland T. Rust. 1984. “Measuring the Congruence of Market Areas.”Journal of Marketing 48: 68–74.

    Article  Google Scholar 

  • MacKay, David B. 1973. “Spatial Measurement of Retail Store Demand.”Journal of Marketing Research 10: 443–453.

    Google Scholar 

  • Mosteller, F. and John W. Tuckey. 1968. “Data Analysis including Statistics.” InHandbook of Social Psychology, Volume 2. Eds. G. Lindzey and E. Aronson. Reading, MA: Addison Wesley.

    Google Scholar 

  • Parzen, E. 1962. “On Estimating of Probability Density Functions and the Mode.”Annals of Mathematical Statistics 33: 1065–1076.

    Google Scholar 

  • — 1979. “Nonparametric Statistical Data Modeling.”Journal of American Statistical Association 74: 105–131.

    Article  Google Scholar 

  • Peterson, Robert A. 1974. “Trade Area Analysis Using Trend Surface Analysis.”Journal of Marketing Research 11: 338–342.

    Article  Google Scholar 

  • Rosenblatt, M. 1956. “Remarks on Some Non-Parametric Estimates of Density Function.”Annals of Mathematical Statistics 27: 832–837.

    Google Scholar 

  • — 1971. “Curve Estimates.”Annals of Mathematical Statistics 42: 1815–1842.

    Google Scholar 

  • Rust, Roland T. and David C. Schmittlein. 1985. “A Bayesian Cross-Validated Likelihood Method for Comparing Alternative Specifications of Qualitative Models.”Marketing Science 4: 20–40.

    Article  Google Scholar 

  • Rust, Roland T. and Julia A. N. Brown. 1986. “Estimation and Comparison of Market Area Densities.”Journal of Retailing 62: 410–430.

    Google Scholar 

  • Silverman, B. W. 1978. “Choosing Window Width When Estimating Density.”Biometriks 65: 1–11.

    Article  Google Scholar 

  • — 1986.Density Estimation for Data Analysis and Statistics. New York: Chapman and Hall.

    Google Scholar 

  • Stone, M. 1974. “Cross-Validatory Choice and Assessment of Statistical Predictions.”Journal of the Royal Statistical Society B 36: 111–147.

    Google Scholar 

  • Wegman, E. J. 1972. “Nonparametric Density Estimation: A Survey of Available Methods.”Technometrics 14: 533–546.

    Article  Google Scholar 

  • Woodroofe, M. 1974. “On Choosing a Delta-Sequence.”Annals of Mathematical Statistics 41: 1665–1671.

    Google Scholar 

  • Zellner, A. 1971.An Introduction to Bayesian Inference in Econometrics. New York: Wiley.

    Google Scholar 

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Donthu, N. Comparing market areas using kernel density estimation. JAMS 19, 323–332 (1991). https://doi.org/10.1007/BF02726507

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  • DOI: https://doi.org/10.1007/BF02726507

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