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...

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

We propose a class of estimators for the parameters of a GARCH(p, q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maxim...

Semiparametric maximum likelihood estimators have recently been proposed for a class of two-phase, outcome dependent sampling models; e.g. Breslow and Holubkov (1997), Scott and Wild (1998), and Lawless, Wild, and Kalb eisch (1999). The estimators studied by these authors are predicated on the estimates of the underlying covariate distribution being concentrated on the observed covariate values...

Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic properties of maximum likelihood estimators of the parameters of a multiple-change-point model for a general class of models in which the form of the distri...