Estimation of the Derivative of a Density and a Related Regression Curve.

Abstract

Let Y(1),...,Y(n),(Y(1)<Y(2)<...<Y(n)) be the order statistics of a random sample from a distribution F with density f on the real line. This paper gives a class of estimators of the derivative f'(x) of the density f at points x for which f has a continuous second derivative. These estimators are based on spacings in the order statistics Y(j+k(n)) - Y(j), j = 1,...,n-k(n), k(n)<n, and are shown to be consistent under suitably given conditions. These estimators are then used to estimate a related regression curve in a manner similar to Nadaraya (Theory Prob. Appl., 10, 1963, pp. 186-190).

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1976
Accession Number
ADA028229

Entities

People

  • B. K. Kim
  • J. Van Ryzin

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Computing-Related Activities
  • Contracts
  • Cooperation
  • Data Science
  • Estimators
  • Information Science
  • Interdisciplinary Science
  • Mathematics
  • New York
  • Order Statistics
  • Statistical Analysis
  • Statistical Samples
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.

Technology Areas

  • Space
  • Space - Space Objects