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Statistical Inference for the Relative Density

Author

Listed:
  • MARK S. HANDCOCK

    (University of Washington)

  • PAUL L. JANSSEN

    (Limburgs Universitair Centrum, Belgium)

Abstract

Social scientists are increasingly interested in techniques for comparing changes in distributional shape in addition to mean levels. One such technique is based on the relative distribution, a nonparametric summary of the information required for scale-invariant comparisons between two distributions. The relative distribution is being used by social scientists to represent and analyze distributional differences, enabling researchers to move well beyond comparisons of means and variances in a simple intuitive way. The authors develop a nonparametric estimator for the relative density function. They study its asymptotic properties, derive computable expressions for the asymptotic variance, and consider local bandwidth selection. They also illustrate how the relative density can be decomposed into a component due to location differences and a component due to shape differences. This decomposition identifies that component of interdistributional dissimilarity due to interdistributional inequality. The methods are illustrated by comparing the earnings distributions of working women to that of working men based on the 1990 census and to women from 1967 to 1996.

Suggested Citation

  • Mark S. Handcock & Paul L. Janssen, 2002. "Statistical Inference for the Relative Density," Sociological Methods & Research, , vol. 30(3), pages 394-424, February.
    • Handle: RePEc:sae:somere:v:30:y:2002:i:3:p:394-424
    DOI: 10.1177/0049124102030003005
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    References listed on IDEAS

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    1. Jeffrey S. Simonoff, 1998. "Three Sides of Smoothing: Categorical Data Smoothing, Nonparametric Regression, and Density Estimation," International Statistical Review, International Statistical Institute, vol. 66(2), pages 137-156, August.
    2. Cwik, Jan & Mielniczuk, Jan, 1993. "Data-dependent bandwidth choice for a grade density kernel estimate," Statistics & Probability Letters, Elsevier, vol. 16(5), pages 397-405, April.
    3. Butler, Richard J & McDonald, James B, 1987. "Interdistributional Income Inequality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 13-18, January.
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    Cited by:

    1. Rodrigues, Clarissa Guimarães & Rios-Neto, Eduardo Luiz Gonçalves & de Xavier Pinto, Cristine Campos, 2013. "Changes in test scores distribution for students of the fourth grade in Brazil: A relative distribution analysis for the years 1997–2005," Economics of Education Review, Elsevier, vol. 34(C), pages 227-242.
    2. Zoya Nissanov & Maria Grazia Pittau, 2016. "Measuring changes in the Russian middle class between 1992 and 2008: a nonparametric distributional analysis," Empirical Economics, Springer, vol. 50(2), pages 503-530, March.
    3. Elisa–María Molanes-López & Ricardo Cao, 2008. "Relative density estimation for left truncated and right censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 693-720.

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