This manuscript considers inference on a single parameter in a multivariate canonical exponential family, where the effect of nuisance parameters on the p-value is mitigated by conditioning on the event that the sufficient statistics associated with the nuisance parameters lie in a neighborhood...

Saddlepoint methods present a convenient way to approximate probabilities associated with canonical sufficient statistic vectors in generalized linear models. Implementing saddlepoint approximations requires calculating maximum likelihood estimators for the associated parameters. When the...

This paper presents results showing that the error involved in using the double saddlepoint distribution function approximations of Skovgaard (1987,J. Appl. Probab.24875-887) are uniformly bounded. Particular attention is paid to distributions of sufficient statistics arising from generalized...

We discuss inference after data exploration, with a particular focus on inference after model or variable selection. We review three popular approaches to this problem: sample splitting, simultaneous inference, and conditional selective inference. We explain how each approach works and highlight...