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Using Computer-Binned Data for Density Estimation

In: Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface

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  • David W. Scott

    (Rice University)

Abstract

With real time microcomputer monitoring systems or with large data bases, data may be recorded as bin counts to satisfy computer memory constraints and to reduce computational burdens. If the data represent a random sample, then a natural question to ask is whether such binned data may successfully be used for density estimation. Here we consider three density procedures: the histogram, parametric models determined by a few moments, and the nonparametric kernel density estimator of Parzen and Rosenblatt. For the histogram, we show that computer-binning causes no problem as long as the binning is sufficiently smaller than the data-based bin width 3.5σ n−1/3. Another result is that some binning of data appears to provide marginal improvement in the integrated mean squared error of the corresponding kernel estimate. Some examples are given to illustrate the theoretical and visual effects of using binned data.

Suggested Citation

  • David W. Scott, 1981. "Using Computer-Binned Data for Density Estimation," Springer Books, in: William F. Eddy (ed.), Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface, pages 292-294, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-9464-8_42
    DOI: 10.1007/978-1-4613-9464-8_42
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