On the histogram as a density estimator:L2 theory

  • David Freedman
  • Persi Diaconis


Stochastic Process Probability Theory Mathematical Biology Density Estimator 
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  1. Bechenbach, E.F., Bellman, R.: Inequalities, 2nd ed. Berlin-Heidelberg-New York: Springer 1965Google Scholar
  2. Cover, T.: A hierarchy of probability density function estimates. Frontiers of Pattern Recognition. New York: Academic Press 1972Google Scholar
  3. Feller, W.: An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd ed. New York: Wiley 1971Google Scholar
  4. Fryer, M.J.: A review of some non-parametric methods of density estimation. J. Inst. Math. Appl.20, 335–354 (1977)Google Scholar
  5. Knuth, D.: The Art of Computer Programming, Vol. 1, 2nd ed. Reading, Mass.: Addison-Wesley 1973Google Scholar
  6. Rosenblatt, M.: Curve estimates. Ann. Statist.2, 1815–1852 (1971)Google Scholar
  7. Scott, D.: On optimal and data-based histograms. Biometrika66, 605–610 (1979)Google Scholar
  8. Tapia, R.A., Thompson, J.R.: Nonparametric Probability Density Estimation. Baltimore: Johns Hopkins 1978Google Scholar
  9. Tarter, M.E., Kronmal, R.S.: An introduction to the implementation and theory of nonparametric density estimation Amer. Statist.30, 105–111 (1976)Google Scholar
  10. Wegman, E.J.: Nonparametric probability density estimation I. A summary of available methods. Technometrics14, 533–546 (1972)Google Scholar
  11. Wertz, W., Schneider, B.: Statistical density estimation: A bibliography. Internat. Statist Rev.47, 155–175 (1979)Google Scholar
  12. Woodroofe, M.: On choosing a delta sequence. Ann. Math. Statist.41, 1665–1671 (1968)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • David Freedman
    • 1
  • Persi Diaconis
    • 2
  1. 1.Statistics DepartmentUniversity of CaliforniaBerkeleyUSA
  2. 2.Statistics DepartmentStanford UniversityStanfordUSA

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