Accession Number:

ADA364737

Title:

Mu-Estimating and Smoothing

Descriptive Note:

Technical rept.

Corporate Author:

PENNSYLVANIA STATE UNIV UNIVERSITY PARK CENTER FOR MULTIVARIATE ANALYSIS

Personal Author(s):

Report Date:

1999-03-01

Pagination or Media Count:

23.0

Abstract:

In the traditional M-estimation theory developed by Huber 1964, the parameter under estimation is the value of theta which minimizes the expectation of what is called a discrepancy measure DISM delta x, theta which is a function of theta and the underlying random variable X. Such a setting does not cover the estimation of parameters such as multivariate median defined by Oja 1983 and Liu 1990, as the value of theta which minimizes the expectation of a DISM of the type delta X1,... , Xm, theta where X1,... , Xm are independent copies of the underlying random variable X. Arcones et al 1994 studied the estimation of such parameters. We call the associated M-estimation MU-estimation or mu-estimation for convenience. When a DISM is not a differentiable function of theta, some complexities arise in studying the properties of estimations as well as in their computation. In such a case we introduce a new method of smoothing the DISM with a kernel function and using it in estimation. It is seen that smoothing allows up to develop an elegant approach to the study of asymptotic properties and computation of estimations.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE