Adaptive empirical Bayesian smoothing splines

In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the model. The selected order and smoothing parameter are used to construct adaptive credible sets with good frequentist coverage for the underlying regression function. We use these credible sets as a proxy to show the superior performance of adaptive empirical Bayesian smoothing splines compared to frequentist smoothing splines

Uniformly Valid Inference Based on the Lasso in Linear Mixed Models

Linear mixed models (LMMs) are suitable for clustered data and are common in e.g. biometrics, medicine, or small area estimation. It is of interest to obtain valid inference after selecting a subset of available variables. We construct confidence sets for the fixed effects in Gaussian LMMs that are estimated via a Lasso-type penalization which allows quantifying the joint uncertainty of both variable selection and estimation. To this end, we exploit the properties of restricted maximum likelihood (REML) estimators to separate the estimation of the regression coefficients and covariance parameters. We derive an appropriate normalizing sequence to prove the uniform Cramer consistency of the REML estimators. We then show that the resulting confidence sets for the fixed effects are uniformly valid over the parameter space of both the regression coefficients and the covariance parameters. Their superiority to naive post-selection least-squares confidence sets is validated in simulations and illustrated with a study of the acid neutralization capacity of U.S. lakes.Comment: 22 pages, 1 figur

On threshold estimation in threshold vector error correction models

Resource /Energy Economics and Policy,

Joint non-parametric estimation of mean and auto-covariances for Gaussian processes

Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions of such processes is developed. The proposed empirical Bayes approach is data-driven, numerically efficient, and allows for the construction of confidence sets for the mean function. Performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc