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Transformations for Smooth Regression Models with Multiplicative Errors

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  • G. K. Eagleson
  • H. G. Müller

Abstract

We consider whether one should transform to estimate nonparametrically a regression curve sampled from data with a constant coefficient of variation, i.e. with multiplicative errors. Kernel‐based smoothing methods are used to provide curve estimates from the data both in the original units and after transformation. Comparisons are based on the mean‐squared error (MSE) or mean integrated squared error (MISE), calculated in the original units. Even when the data are generated by the simplest multiplicative error model, the asymptotically optimal MSE (or MISE) is surprisingly not always obtained by smoothing transformed data, but in many cases by directly smoothing the original data. Which method is optimal depends on both the regression curve and the distribution of the errors. Data‐based procedures which could be useful in choosing between transforming and not transforming a particular data set are discussed. The results are illustrated on simulated and real data.

Suggested Citation

  • G. K. Eagleson & H. G. Müller, 1997. "Transformations for Smooth Regression Models with Multiplicative Errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 173-189.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:1:p:173-189
    DOI: 10.1111/1467-9868.00062
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    Cited by:

    1. Van Keilegom, Ingrid, 2013. "Discussion on: "An updated review of Goodness-of-Fit tests for regression models" (by W. Gonzales-Manteiga and R.M. Crujeiras)," LIDAM Discussion Papers ISBA 2013008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Dette, Holger & Wieczorek, Gabriele, 2007. "Testing for a constant coefficient of variation in nonparametric regression," Technical Reports 2007,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Escanciano, Juan Carlos & Pardo-Fernandez, Juan Carlos & Van Keilegom, Ingrid, 2015. "Asymptotic distribution-free tests for semiparametric regressions," LIDAM Discussion Papers ISBA 2015001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Xuehai Zhang, 2019. "A Box-Cox semiparametric multiplicative error model," Working Papers CIE 125, Paderborn University, CIE Center for International Economics.
    5. Xuehai Zhang, 2019. "A Box-Cox semiparametric multiplicative error model," Working Papers CIE 122, Paderborn University, CIE Center for International Economics.
    6. Holger Dette & Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2009. "Goodness‐of‐Fit Tests for Multiplicative Models with Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 782-799, December.

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