Accession Number : AD0710751

Title :   THE BEHAVIOR OF ROBUST ESTIMATORS ON DEPENDENT DATA,

Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s) : Rubin,Herman ; Gastwirth,Joseph L.

Report Date : AUG 1969

Pagination or Media Count : 104

Abstract : The report studies the effect of serial dependence on the efficiency of various robust estimators of the location parameter. In order to show that the asymptotic distribution of these estimators is a normal distribution a slightly stronger mixing condition than Rosenblatt's strong mixing is introduced and it is shown that the empiric c.d.f. formed from such a process approaches a Gaussian process. In particular, first order autoregressive processes with Gaussian, Cauchy and double-exponential marginal distributions are shown to obey the conditions. The behavior of robust estimators on Gaussian processes is studied in greater detail. One general result states that for any Gaussian process with serial correlation (rho sub k) > 0 and summation (rho sub k) < infinity, the efficiency of any linear combination of the order statistics relative to the sample mean is greater than its efficiency in the case of independent observations. The same result holds for the Hodges-Lehmann estimator. These results are applied to two models of contamination and show that the estimators which have been developed to be robust against outliers are robust against dependence. (Author)

Descriptors :   (*STATISTICAL ANALYSIS, DECISION THEORY), STOCHASTIC PROCESSES, TIME SERIES ANALYSIS, EXPONENTIAL FUNCTIONS, STATISTICAL DISTRIBUTIONS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE