Nearest neighbor imputation (NNI) is a popular imputation method used to compensate for item nonresponse in sample surveys. Although previous results showed that the NNI sample mean and quantiles are consistent estimators of the population mean and quantiles, large sample inference procedures, such as asymptotic confidence intervals for the population mean and quantiles, are not available. For ...

Sydney, NSW 2109, Australia Abstract This paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles. Our estimators are linear combinations of M-estimators. Their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators. Compared with empirical quantiles, the new estimators...

In this paper we propose a method to robustly estimate linear regression quantiles with censored data. We adjust the estimator recently developed by Portnoy by replacing the Koenker-Bassett regression quantiles with the regression depth quantiles. The resulting optimization problem is solved iteratively over a set of grid points. We show on some examples that, contrary to the Koenker-Bassett ap...

• Central properties of geometric quantiles have been well-established in the recent statistical literature. In this study, we try to get a grasp of how extreme geometric quantiles behave. Their asymptotics are provided, both in direction and magnitude, under suitable moment conditions, when the norm of the associated index vector tends to one. Some intriguing properties are highlighted: in par...

In this technical report a notion of (lower) quantiles for data or random variables with values in a complete lattice is developed. We list a number of desirable properties a reasonable notion of quantiles should have and analyze for different proposals of quantiles, which of these properties they fulfill. It turns out that one of the constructions has acceptable properties and can thus be used...

This paper sheds some new light on the multivariate (projectional) quantiles recently introduced in Kong and Mizera (2008). Contrary to the sophisticated set analysis used there, we adopt a more parametric approach and study the subgradient conditions associated with these quantiles. In this setup, we introduce Lagrange multipliers which can be interpreted in various interesting ways. We also l...

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The estimation of extreme conditional quantiles is an important issue in different scientific disciplines. Up to now, the extreme value literature focused mainly on estimation procedures based on i.i.d. samples. On the other hand, quantile regression based procedures work well for estimation within the data range i.e. the estimation of nonextreme quantiles but break down when main interest is i...