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Density estimation: Are theoretical results useful in practice? (English) Zbl 0601.62056

Asymptotic theory of statistical tests and estimation, Proc. Int. Symp., Chapel Hill/NC 1979, 179-203 (1980).
[For the entire collection see Zbl 0428.00021.]
Theoreticians in statistics often lose sight of the basic aim of statistics, the analysis of data. One of the most fundamental statistical concepts is the probability density function, and estimates of this function are of enormous importance in data analysis. Probability density estimates have been studied by an enormous number of authors, but there has been little attempt to reconcile theory and practice.
In this paper, some reasons for estimating densities are discussed, after which the possible application of theoretical work to provide a practical method for determining how much to smooth a given data set is considered. The method ultimately obtained is objective and is applied to some engineering data.

MSC:

62G05 Nonparametric estimation

Citations:

Zbl 0428.00021