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The roles of ISE and MISE in density estimation

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  • Jones, M. C.

Abstract

There is disagreement in the literature concerning the roles of integrated squared error (ISE) and mean integrated squared error (MISE) in kernel density estimation. The issues are reviewed. If best estimation of the underlying density is truly considered to be the objective, conclusions are that ISE is more appropriate than MISE for assessing the performance of density estimates using data-based bandwidth choices and, relatedly, that, in choosing bandwidths initially, aiming for the ISE-optimal bandwidth is more appropriate than aiming for the MISE-optimal target. However, it turns out that practical procedures based on MISE considerations remain one particularly sensible way to go about making automatic bandwidth selections aimed at the ISE-optimal target. Moreover, it is then argued that hoping to be able to estimate a density well from every data set associated with it is unrealistic and that one can only expect to do well in some average sense. This leads back to a conceptual preference for MISE-related procedures, a viewpoint the author commends for general use.

Suggested Citation

  • Jones, M. C., 1991. "The roles of ISE and MISE in density estimation," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 51-56, July.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:1:p:51-56
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    Citations

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    Cited by:

    1. Scott Fortmann-Roe & Richard Starfield & Wayne M Getz, 2012. "Contingent Kernel Density Estimation," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-10, February.
    2. Duc Devroye & J. Beirlant & R. Cao & R. Fraiman & P. Hall & M. Jones & Gábor Lugosi & E. Mammen & J. Marron & C. Sánchez-Sellero & J. Uña & F. Udina & L. Devroye, 1997. "Universal smoothing factor selection in density estimation: theory and practice," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(2), pages 223-320, December.
    3. Yi Jin & Yulin He & Defa Huang, 2021. "An Improved Variable Kernel Density Estimator Based on L 2 Regularization," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    4. Berwin A. TURLACH, "undated". "Bandwidth selection in kernel density estimation: a rewiew," Statistic und Oekonometrie 9307, Humboldt Universitaet Berlin.
    5. Wang, Qing & Lindsay, Bruce G., 2015. "Improving cross-validated bandwidth selection using subsampling-extrapolation techniques," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 51-71.
    6. Zhenyu Jiang & Nengxiang Ling & Zudi Lu & Dag Tj⊘stheim & Qiang Zhang, 2020. "On bandwidth choice for spatial data density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 817-840, July.
    7. Lawrence Dacuycuy, 2007. "On wage density comparisons: bandwidth selectors and test outcomes," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 203-208.
    8. Mercedes Conde-Amboage & César Sánchez-Sellero, 2019. "A plug-in bandwidth selector for nonparametric quantile regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 423-450, June.
    9. Xia, Yingcun & Li, W. K., 2002. "Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 265-287, November.
    10. Miguel Reyes & Mario Francisco-Fernández & Ricardo Cao, 2017. "Bandwidth selection in kernel density estimation for interval-grouped data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 527-545, September.
    11. Zudi Lu & Dag Johan Steinskog & Dag Tjøstheim & Qiwei Yao, 2009. "Adaptively varying‐coefficient spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 859-880, September.

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