On the histogram as a density estimator:L2 theory

  title={On the histogram as a density estimator:L2 theory},
  author={David Freedman and Persi Diaconis},
  journal={Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und Verwandte Gebiete},
  • D. Freedman, P. Diaconis
  • Published 1981
  • Mathematics
  • Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Let f be a probability density on an interval I, finite or infinite: I includes its finite endpoints, if any; and f vanishes outside of I. Let X1, . . . ,X k be independent random variables, with common density f The empirical histogram for the X's is often used to estimate f To define this object, choose a reference point xosI and a cell width h. Let Nj be the number of X's falling in the j th class interval: 
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