An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its...

By assuming that the underlying distribution belongs to the domain of attraction of an extreme value distribution, one can extrapolate the data to a far tail region so that a rare event can be predicted. However, when the distribution is in the domain of attraction of a Gumbel distribution, the...

In the literature on analyzing extremes, both generalized Pareto distributions and Pareto distributions are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ...