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This paper investigates the focused information criterion and plug-in average for vector autoregressive models with local-to-zero misspecification. These methods have the advantage of focusing on a quantity of interest rather than aiming at overall model fit. Any (sufficiently regular) function of the parameters can be used as a quantity of interest. We determine the asymptotic properties and elaborate on the role of the locally misspecified parameters. In particular, we show that the inability to consistently estimate locally misspecified parameters translates into suboptimal selection and averaging. We apply this framework to impulse response analysis. A Monte Carlo simulation study supports our claims. [ABSTRACT FROM AUTHOR]

This article is concerned with variable selection methods for the Cox proportional hazards regression model. Including excessive covariates causes extra variability and inflated confidence intervals for regression parameters; thus regimes for discarding the less informative ones are needed. Our framework has p covariates designated as "protected," while variables from a further set of q covariates are examined for possible inclusion or exclusion. We develop a focused information criterion (FIC) that for given interest parameter finds the best subset of covariates. Thus the FIC might find that the best model for predicting median survival time is different than the best model for estimating survival probabilities, and the best overall model for analyzing men's survival might not be the same as the best overall model for analyzing women's survival. Methodology is also developed for model averaging, wherein the final estimate of a quantity is a weighted average of estimates computed for a range of submodels. Our methods are illustrated in simulations and for a survival study of Danish skin cancer patients. [ABSTRACT FROM AUTHOR]