ARMA Estimators of Probability Densities with Exponential or Regularly Varying Fourier Coefficients.

Abstract

Properties of a probability density estimator having the rational form of a ARMA spectrum are investigated. Under various conditions on the underlying density's Fourier coefficients, the ARMA estimator is shown to have asymptotically smaller mean integrated squared error (MISE) than the best window-type Fourier series estimator. The most interesting cases are those in which the Fourier coefficients are regularly varying with index-p,p > 1/2. For example, when p=2 the asymptotic MISE of a certain ARMA estimator is only about 75% of that for the optimum window estimator. For a density f with support in 0, PI, the condition p=2 occurs whenever f'(0+) does not equal to 0, f' (pi-) =0, and f is square integrable. Keywords: Generalized jackknife; Regularly varying function.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1987
Accession Number
ADA182552

Entities

People

  • Jeffrey D. Hart

Organizations

  • Texas A&M University

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Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Coefficients
  • Convergence
  • Data Science
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  • Estimators
  • Fourier Series
  • Information Science
  • Military Research
  • Probability
  • Probability Density Functions
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Fields of Study

  • Mathematics

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  • Approximation Theory.
  • Statistical inference.