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...

Standard approximate 1-a 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-a. Alternatively, this adjustment...