Mu-Estimating and Smoothing
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1999
- Accession Number
- ADA364737
Entities
People
- Calyampudi Radhakrishna Rao
- Z. J. Liu
Organizations
- Pennsylvania State University