Effect of correlation on the estimation of a mean in the presence of spurious observations

Abstract : This paper examines the effect of various correlation structures of observations on rules for estimating a mean which are designed to quard against the possibility of spurious observations (that is, observations generated in a manner not intended). The premium and protection of these rules are evaluated and discussed for the equi-correlation case and for the case of an autoregressive process of first order. It is shown that the premium and protection of a given rule which is designed for the estimator of a general mean mu when spuriosity may exist and when the observations are independent, lacks robustness to departures from independence. It is also shown that in moderate sized samples a spurious observation could seriously bias the usual estimator of the autoregressive coefficient alpha. One application of these results is in the case of a first order autoregressive model which can be used to represent many time series data encountered in business and economics.