Interval estimation via tail functions

In this paper we describe a new methodology for constructing confidence intervals. The idea is to specify the tail cutoff areas in terms of a function of the target parameter rather than as constants. This function, called the tail function, can be engineered so as to provide shorter confidence intervals when prior information is available. It can also be used to improve the coverage properties of approximate confidence intervals. We illustrate the methodology by applying it to inference on the normal mean and binomial proportion, and develop measures of the resulting improvements. Guidelines for choosing the optimal tail function in any situation are provided, and the relationship with Bayesian inference is discussed

The health expectancies of older Australians

Based on the Australian Bureau of Statistics surveys of 1981, 1988, 1993 and 1998 the paper present estimates of health expectancies of the states Disability-free and Disabled, for females and males aged 60 and over by cohort from 1980, and current for the survey years. Recently developed logistic regression techniques are used instead of the standard methods due to Sullivan, and a major aim of this report is to present these techniques in a readily useable form. An informal presentation of the approach is given in Section 2, with a more rigorous methodological exposition in Section 4. Section 3 contains graphical and numerical results. Amongst our findings is that the results of the three later surveys are broadly similar and differ in important respects from those of the 1981 survey. Based on the last three surveys our estimates support the view that, depending on age, roughly two thirds or more of the increase in life expectancy over the decade 1988-1998 is taken in a state of disability. Also, our findings do not support rectangularisation of the survival or disability-free survival curve