# Accession Number:

## ADA028229

# Title:

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

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1976-03-01

# Pagination or Media Count:

## 17.0

# Abstract:

Let Y1,...,Yn,Y1Y2...Yn 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 fx 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 Yjkn - Yj, j 1,...,n-kn, knn, 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability