We present a new and simple method for constructing a 1-[alpha] upper confidence limit for [theta] in the presence of a nuisance parameter vector [psi], when the data is discrete. Our method is based on computing a P-value P{T[less-than-or-equals, slant]t} from an estimator T of [theta],...

We consider exact confidence limits obtained from discrete data by inverting a hypothesis test based on a studentized test statistic. We show that these confidence limits (a) are nesting and (b) have greater large sample efficiency than Buehler confidence limits that are required to be nesting.

Consider a two-treatment, two-period crossover trial, with responses that are continuous random variables. We find a large-sample frequentist 1-[alpha] confidence interval for the treatment difference that utilizes the uncertain prior information that there is no differential carryover effect.

Consider the reliability problem of finding a 1-[alpha] upper (lower) confidence limit for [theta] the probability of system failure (non-failure), based on binomial data on the probability of failure of each component of the system. The Buehler 1-[alpha] confidence limit is usually based on an...

In 1957, R.J. Buehler gave a method of constructing honest upper confidence limits for a parameter that are as small as possible subject to a pre-specified ordering restriction. In reliability theory, these 'Buehler bounds' play a central role in setting upper confidence limits for failure...

Standard approximate 1 - &agr; prediction intervals (PIs) need to be adjusted to take account of the error in estimating the parameters. This adjustment may be aimed at setting the (unconditional) probability that the PI includes the value being predicted equal to 1 - &agr;. Alternatively, this...

A new simulation-based prediction limit that improves on any given estimative d-step-ahead prediction limit for a Markov process is described. This improved prediction limit can be found with almost no algebraic manipulations. Nonetheless, it has the same asymptotic coverage properties as the...

The Buehler 1-[alpha] upper confidence limit is as small as possible, subject to the constraints that (a) its coverage probability never falls below 1-[alpha] and (b) it is a non-decreasing function of a designated statistic T. We provide two new results concerning the influence of T on the...

Using an algorithm of Joffe (Ann. Probab. 2 (1974) 161-162) we generate a finite sequence of 4-independent random variables. Using this sequence we find a confidence interval with coverage probability exceeding a value close to 1-[alpha] for [theta]=E{g(U)} where U=(U1,...,Us) with U1,...,Us...