# Accession Number:

## ADA070205

# Title:

## Asymptotic Distributions of Slope of Greatest Convex Minorant Estimators.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1979-04-01

# Pagination or Media Count:

## 27.0

# Abstract:

Isotonic estimation involves the estimator of a function which is known to be increasing with respect to a specified partial order. For the case of a linear order, a general theorem is given which simplifies and extends the techniques of Prakasa Rao 1966 and Brunk 1970. Sufficient conditions for a specified limit distribution to obtain are expressed in terms of a local condition and a global condition. The theorem is applied to several examples. The first example is estimation of a monotone function mu on 0,1 based on observations in, X sub ni, where EX sub ni mu in. In the second example, in is replaced by random T sub ni. Robust estimators for this problem are described. Estimation of a monotone density function is also discussed. It is shown that the rate of convergence depends on the order of first non-zero derivative and that this result can obtain even if the function is not monotone over its entire domain. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability