Journal of Official Statistics, Vol.7, No.2, 1991. pp. 219233

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Model-Free Curve Estimation: Mutuality and Disparity of Approaches

This paper is written to provide methodological background for researchers interested in applying curve estimation to fields such as environmental health. Basic approaches are introduced with special emphasis on shared features which may be of value in environmental and other investigations. Completeness and generality from the viewpoint of curve estimation are described as are new applications to non-parametric inference and mixture decomposition. Series, kernel, and penalized likelihood methodologies are compared as are different metrics and methods of counter-balancing representational complexity with data availability.

Curve estimation methodology is illustrated as a way of uncovering distributional bimodality. The danger inherent in relying on conventional parametric procedures is demonstrated by the case of an anomalous model, the log-Cauchy, which gives the false appearance of being a mixture model. The potential value of the new approach is illustrated by hybrid procedures which combine nonparametric estimation and rank-based inferential methodology.

Bump-hunting; Chi-square goodness-of-fit; decomposition; kernels; mean integrated square error; mixing parameters; multipliers; penalized likelihood; series.

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