A note on the joint distribution of correlated quadratic forms

In the present paper, the authors obtained exact and asymptotic expressions for the joint distribution of correlated quadratic forms when the underlying distribution is a multivariate normal.     

Regression of area mortality rates on explanatory variables: what weighting is appropriate?

"One can often gain insight into the aetiology of a disease by relating mortality rates in different areas to explanatory variables. Multiple regression techniques are usually employed, but unweighted least squares may be inappropriate if the areas vary in population size. Also, a fully weighted regression, with weights inversely proportional to binomial sampling variances, is usually too extreme. This paper proposes an intermediate solution via maximum likelihood which takes account of three sources of variation in death rates: sampling error, explanatory variables and unexplained differences between areas. The method is also adapted for logit (death rates), standardized mortality ratios (SMRs) and log (SMRs). Two [United Kingdom] examples are presented."     

LOGISTIC REGRESSION COMPARED TO NORMAL DISCRIMINATION FOR NON-NORMAL POPULATIONS'

An investigation is undertaken of the logistic regression procedure for estimating the posterior probability of an object belonging to one of two populations. The asymptotic bias and mean square error associated with the procedure are derived for univariate populations whose distributions satisfy the general Day-Kerridge model for which the logistic form is valid for the posterior probability. These properties are compared with those of the normal discrimination method based on the classical assumption of normal populations with common variances. The asymptotic relative efficiency of logistic regression is considered on the basis of asymptotic mean square error.     

A dynamic Mover–Stayer model for recurrent event processes subject to resolution

In studies of affective disorder, individuals are often observed to experience recurrent symptomatic exacerbations warranting hospitalization. Interest may lie in modeling the occurrence of such exacerbations over time and identifying associated risk factors. In some patients, recurrent exacerbations are temporally clustered following disease onset, but cease to occur after a period of time. We develop a dynamic Mover–Stayer model in which a canonical binary variable associated with each event indicates whether the underlying disease has resolved. An individual whose disease process has not resolved will experience events following a standard point process model governed by a latent intensity. When the disease process resolves, the complete data intensity becomes zero and no further event will occur. An expectation–maximization algorithm is described for parametric and semiparametric model fitting based on a discrete time dynamic Mover–Stayer model and a latent intensity-based model of the underlying point process.