ON SOME ROBUST ESTIMATORS BASED ON NON-DISTRIBUTION-FREE $ U $ STATISTICS

Distribution Free Confidence Intervals for Quantiles Based on Extreme Order Statistics in a Multi-Sampling Plan

Extended Abstract. Let Xi1 ,..., Xini   ,i=1,2,3,....,k  be independent random samples from distribution $F^{alpha_i}$،  i=1,...,k, where F is an absolutely continuous distribution function and $alpha_i>0$ Also, suppose that these samples are independent. Let Mi,ni and  M'i,ni  respectively, denote the maximum and minimum of the ith sa...

U-Statistics Based on Spacings

In this paper, we investigate the asymptotic theory for U -statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U -statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit th...

Inferences for Extended Generalized Exponential Distribution based on Order Statistics

‎Recently‎, ‎a new distribution‎, ‎named as extended generalized exponential distribution‎, ‎has been introduced by Kundu and Gupta (2011). ‎In this paper‎, ‎we consider the extended generalized exponential distribution with known shape parameters α and β. ‎At first‎, ‎the exact expressions for marginal and product moments of o...

Confidence Intervals Based on Robust Estimators

Robust estimation of U-statistics

An important part of the legacy of Evarist Giné is his fundamental contributions to our understanding of U -statistics and U -processes. In this paper we discuss the estimation of the mean of multivariate functions in case of possibly heavy-tailed distributions. In such situations, reliable estimates of the mean cannot be obtained by usual U -statistics. We introduce a new estimator, based on t...