Curve Estimates

  • Richard A. Davis
  • Keh-Shin Lii
  • Dimitris N. Politis
Chapter
Part of the Selected Works in Probability and Statistics book series (SWPS)

Abstract

There is a large class of problems in which the estimation of curves arises naturally (see [15], [34]). It is curious that one of the earliest extensive investigations of this type involves the estimation of the spectral density function when sampling from a stationary sequence ([1], [17], [27], [33]). Even though the simple histogram has been used for years, it was only later that the simpler question of estimating a probability density function was dealt with at some length ([26], [25], [9]). Because the final character of the usual results obtained in both problem areas is quite similar, and the arguments are much more transparent in the case of the probability density function, we shall develop the results for the probability density function first. Later some corresponding results for spectra will be given.

Keywords

Manifold Covariance 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Richard A. Davis
    • 1
  • Keh-Shin Lii
    • 2
  • Dimitris N. Politis
    • 3
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of StatisticsUniversity of CaliforniaRiversideUSA
  3. 3.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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