# Accession Number:

## AD0661353

# Title:

## CONTRIBUTIONS TO ROBUST ESTIMATION,

# Descriptive Note:

# Corporate Author:

## NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1967-09-01

# Pagination or Media Count:

## 133.0

# Abstract:

For the problem of efficiency-robust estimation of the location parameter theta of a family of symmetric pdfs fx-thetavertical line lambda, lambda epsilon Lambda 1,...,m, theta epsilon Theta theta such that minus infinity theta infinity, the method of mixture models of Birnbaum is applied to determine generalized Pitman estimators, which are shown to be admissible, with squared error loss function, under broad regularity conditions. With increasing sample size, these estimators are proved to be fully efficient i.e., asymptotically equivalent, for each value of lambda, to the maximum likelihood estimator which would be appropriate if the true value of lambda were known. Computationally tractable analogous estimators based on k sample quantiles are defined in the context of the model representing their asymptotic normal distributions. It is shown that with increasing k these approach equivalence to the fully efficient estimators based on complete samples. Equivalent estimators are given also for the case of unknown scale parameters. Efficiency-robust linear unbiased estimators based on sample quantiles are derived and the optimal spacing of quantiles is discussed. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability