Risto Heijmans

Consistent maximum-likelihood estimation with dependent observations : The general (non-normal) case and the normal case

Abstract In this paper we aim to establish intuitively appealing and verifiable conditions for the existence and weak consistency of ML estimators in a multi-parameter framework, assuming neither the independence nor the identical distribution of the observations. The paper has two parts. In the first part (Theorems 1 and 2) we assume that the joint density of the observations is known (except for the values of a finite number of parameters to be estimated), but we do not specify this distribution. In the second part (Theorems 3–6), we do specify the distribution and assume joint normality (but not independence) of the observations. Some examples are also provided.

When does the expectation of a ratio equal the ratio of expectations

In this paper we investigate the behaviour of a ratio of random variables and try to find conditions under which, this expectation equals the ratio of expectations.

Estimation of the SURE model

The paper presents the essentials of the SURE model and the estimation of its parameters β and ω. Two alternative compact representations of the model are being used. The parameter β is estimated by least squares (LS), generalized least squares (GLS) and maximum likelihood (ML) (under normality).For ω two estimators are being considered, viz an LS-related estimator and a maximum likelihood estimator (under normality). Attention is being given to the study of asymptotic properties of all estimators examined. It turns out that the LS-related and ML estimators of ω follow the same asymptotic (normal) distribution.Efficiency comparisons for the various estimators of β conclude the paper.