Empirical Likelihood Method For Intermediate Quantiles

Adjusted Empirical Likelihood Method for Quantiles

On M-estimators and normal quantiles

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...

Smoothed weighted empirical likelihood ratio confidence intervals for quantiles

Thus far, likelihood-based interval estimates for quantiles have not been studied in the literature on interval censored case 2 data and partly interval censored data, and, in this context, the use of smoothing has not been considered for any type of censored data. This article constructs smoothed weighted empirical likelihood ratio confidence intervals (WELRCI) for quantiles in a unified frame...

On M-estimators of Approximate Quantiles and Approximate Conditional Quantiles

M-estimators introduced in Huber (1964) provide a class of robust estimators of a center of symmetry of a symmetric probability distribution which also have very high eeciency at the model. However it is not clear what they do estimate when the probability distributions are nonsymmetric. In this paper we rst show that in the case of arbitrary, not necessarily symmetric probabilty distributions,...

Bayesian Quantile Regression Methods∗

This paper is a study of the application of Bayesian Exponentially Tilted Empirical Likelihood to inference about quantile regressions. In the case of simple quantiles we show the exact form for the likelihood implied by this method and compare it with the Bayesian bootstrap and with Jeffreys’ method. For regression quantiles we derive the asymptotic form of the posterior density. We also exami...