Consider X1,X2,...,Xn that are independent and identically N([mu],[sigma]2) distributed. Suppose that we have uncertain prior information that [mu]=0. We answer the question: To what extent can a frequentist 1-[alpha] confidence interval for [mu] utilize this prior information?

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...

Pötscher (1991, <italic>Econometric Theory</italic>7, 163–181) has recently considered the question of how the use of a model selection procedure affects the asymptotic distribution of parameter estimators and related statistics. An important potential application of such results is to the generation of...

Consider a linear regression model. Fan and Li (2001) describe the smoothly clipped absolute deviation (SCAD) point estimator of the regression parameter vector. To gain insight into the properties of this estimator, they consider an orthonormal design matrix and focus on the estimation of a...

Casella, Hwang and Robert, Statistica Sinica, 1993, consider a loss function that is a linear combination of the interval length and the indicator function that this interval includes the parameter of interest. They show that this leads to a confidence interval for the normal mean with...

It is very common in applied frequentist ("classical") statistics to carry out a preliminary statistical (i.e. data-based) model selection by, for example, using preliminary hypothesis tests or minimizing AIC. This is usually followed by the inference of interest, using the same data, based on...

Suppose that X1,...,Xn are independent and identically N([mu],[sigma]2) distributed, where [mu] and [sigma] are unknown parameters ( and [sigma]>0). We prove that the usual confidence interval for [mu] is admissible within a broad class of confidence intervals.

We consider the Barndorff-Nielsen and Cox (1994, p. 319) method of modifying an estimative prediction interval to obtain an improved prediction interval with better conditional coverage properties. The parameter estimator, on which this improved interval is based, is assumed to have the same...

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...