Bayesian regression analysis has great importance in recent years, especially the Regularization method, Such as ridge, Lasso, adaptive lasso, elastic net methods, where choosing prior distribution of interested parameter is main idea analysis. By penalizing model, variance estimators are reduced notable and bias getting smaller. The tradeoff between penalized estimator consequently produce mor...

An Appendix with proofs and tuning details has been added here. Abstract Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a fundamentally important case where some of the observations do not represent the exac...

An exposition on the use of O’Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O’Sullivan penalized splines are similar to P-splines, but have the advantage of being a direct generalization of smoothing splines. Exact expressions for the O’Sullivan penalty matrix are obtained. Comparisons between the two types o...

This paper studies the outlier detection problem from the point of view of penalized regressions. Our regression model adds one mean shift parameter for each of the n data points. We then apply a regularization favoring a sparse vector of mean shift parameters. The usual L1 penalty yields a convex criterion, but we find that it fails to deliver a robust estimator. The L1 penalty corresponds to ...

A new regularization method for regression models is proposed. The criterion to be minimized contains a penalty term which explicitly links strength of penalization to the correlation between predictors. As the elastic net, the method encourages a grouping effect where strongly correlated predictors tend to be in or out of the model together. A boosted version of the penalized estimator, which ...

Sparse partial correlation is a useful connectivity measure for brain networks, especially, when it is hard to compute the exact partial correlation due to the small-n large-p situation. In this paper, we consider a sparse linear regression model with a l1-norm penalty for estimating sparse brain connectivity based on the partial correlation. For the numerical experiments, we construct the spar...

We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achie...

Likelihood-based inference of odds ratios in logistic regression models is problematic for small samples. For example, maximum-likelihood estimators may be seriously biased or even non-existent due to separation. Firth proposed a penalized likelihood approach which avoids these problems. However, his approach is based on a prospective sampling design and its application to case-control data has...

s Service (CAS) registry number. In the simulation studies, we consider the mass spectra extracted from the NIST Chemistry WebBook (NIST library) as a reference library and the repetitive library as query (experimental) data. In addition, since we assume that the NIST library has the mass spectrum information for all the