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In this article, a method is proposed to get the limiting distributions and asymptotic properties of estimators based on the minimum and/or maximum of a given srs of a truncated distribution. Following a common outline, a review is carried out by considering different kinds of truncated distributions, some new results are also developed. [ABSTRACT FROM AUTHOR]

Influential units occur frequently in surveys, especially in business surveys that collect economic variables whose distributions are highly skewed. A unit is said to be influential when its inclusion or exclusion from the sample has an important impact on the sampling error of estimates. We extend the concept of conditional bias attached to a unit and propose a robust version of the double expansion estimator, which depends on a tuning constant. We determine the tuning constant that minimizes the maximum estimated conditional bias. Our results can be naturally extended to the case of unit nonresponse, the set of respondents often being viewed as a second-phase sample. A robust version of calibration estimators, based on auxiliary information available at both phases, is also constructed. [ABSTRACT FROM AUTHOR]

We argue that the conditional bias associated with a sample unit can be a useful measure of influence in finite population sampling. We use the conditional bias to derive robust estimators that are obtained by downweighting the most influential sample units. Under the model-based approach to inference, our proposed robust estimator is closely related to the well-known estimator of Chambers (1986). Under the design-based approach, it possesses the desirable feature of being applicable with most sampling designs used in practice. For stratified simple random sampling, it is essentially equivalent to the estimator of Kokic & Bell (1994). The proposed robust estimator depends on a tuning constant. In this paper, we propose a method for determining the tuning constant and show that the resulting estimator is consistent. Results from a simulation study suggest that our approach improves the efficiency of standard nonrobust estimators when the population contains units that may be influential if selected in the sample. [ABSTRACT FROM AUTHOR]

In non-regular cases when the regularity conditions does not hold, the Chapman-Robbins (1951) inequality for the variance of unbiased estimators is well known, but the lower bound by the inequality is not attainable. In this article, we extend the Kiefer-type information inequality applicable to the non-regular case to the asymptotic situation, and we apply it to the case of a family of truncated distributions, in which the lower bound by the Kiefer-type inequality derived from an appropriate prior distribution is attained by the asymptotically unbiased estimator. It also follows from the completeness of the sufficient statistic that the lower bound is asymptotically best. Some examples are also given. [ABSTRACT FROM AUTHOR]

Presents a study that determined the bounds for the maximum likelihood estimator of a sample size in Stirling numbers. Background on Stirling numbers and their application in statistics; Analysis of the ordering of the estimators; Derivation of the bounds for the moments of the maximum likelihood estimator.