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selection operator (Lasso) has also been proposed for VAR shrinkage ( Korobilis 2013 ; Gefang 2014 ). Another strand of the literature has proposed Bayesian variable selection as an alternative way of VAR shrinkage. In general, variable selection techniques refer to a statistical procedure that decides stochastically which of the variables enter the VAR equation and which not, based on information provided by the data. Variable selection can be performed either by imposing a tight prior around zero on some of the VAR coefficients ( George, Sun, and Ni 2008 ; Korobilis

, and therefore more likely to introduce the spurious variables in model (ii). Little formal guidance as to how the practitioner should act in this setting has been provided. In this paper, we refer to variables that only predict the treatment and are not associated with the outcome as treatment predictors. As has been shown by [ 9 ], it is plausible that judicious variable selection may lead to appreciable efficiency gains, and several approaches with this aim have been proposed [ 10 , 11 ]. However, confounder selection methods based on either just the treatment

is downstream of genetic variants in the causal pathway and given the high-dimension and high correlation among gene expression data, there are two important aspects of eQTL, (a) to find associations between a set of genetic variants and gene expression (variable selection), where both genotype and gene expression data could be high-dimensional; and (b) to understand the dependence among genes through expression levels while accounting for the genetic variation information (covariance/network estimation). Variable selection and covariance estimation have

relevant features. Examples include brain imaging studies aimed at identifying brain regions associated with comorbidities or genomic studies focused on discovery of cancer biomarkers. Despite the popularity of matched high dimensional studies, it is quite common for these studies to ignore the matched design used when applying variable selection techniques (e.g., Anglim et al. [ 2 ], Westman et al. [ 3 ]). Failure to account for matching has been shown to decrease variable selection accuracy [ 1 ] and lead to biased results [ 4 ]. Currently, there are several

Volume 10, Issue 1 2011 Article 34 Statistical Applications in Genetics and Molecular Biology High-Dimensional Regression and Variable Selection Using CAR Scores Verena Zuber, University of Leipzig Korbinian Strimmer, University of Leipzig Recommended Citation: Zuber, Verena and Strimmer, Korbinian (2011) "High-Dimensional Regression and Variable Selection Using CAR Scores," Statistical Applications in Genetics and Molecular Biology: Vol. 10: Iss. 1, Article 34. DOI: 10.2202/1544-6115.1730 Bereitgestellt von | Imperial College London Angemeldet Heruntergeladen am

Volume 6, Issue 1 2010 Article 6 The International Journal of Biostatistics A Comparison of Variable Selection Approaches for Dynamic Treatment Regimes Peter Biernot, McGill University Erica E. M. Moodie, McGill University Recommended Citation: Biernot, Peter and Moodie, Erica E. M. (2010) "A Comparison of Variable Selection Approaches for Dynamic Treatment Regimes," The International Journal of Biostatistics: Vol. 6: Iss. 1, Article 6. DOI: 10.2202/1557-4679.1178 A Comparison of Variable Selection Approaches for Dynamic Treatment Regimes Peter Biernot and Erica

) , and Wu et al. (2009) ]. In these applications, the cross-validation procedure is commonly used to select the optimal regularization parameter, which, unfortunately, can not guarantee control of false discoveries. Controlling for false discovery is important as it is extremely costly to validate false discoveries. In settings for large-scale hypothesis testing, Benjamini and Hochberg’s FDR-controlling procedure ( Benjamini & Hochberg, 1995 ) has been widely adopted. However, for penalized high-dimensional variable selections, little work has been done. A major

= 1, then the n 2 samples from Condition c = 2, etc. In this framework, assuming that the mean spectrum $\overline{\boldsymbol{\mu}}=n^{-1}\sum_{n}n_{c}\boldsymbol{\mu}_{c}$ μ ¯ = n − 1 ∑ n n c μ c is set to zero, the problem of determining which metabolites are relevant boils down to finding the non null coefficients in the matrix B and hence can be seen as a variable selection problem in the multivariate linear model. Several approaches can be considered for solving this task: either a posteriori methods such as classical statistical tests in ANOVA

Volume 7, Issue 4 2011 Article 2 Journal of Quantitative Analysis in Sports A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics Blakeley B. McShane, Northwestern University Alexander Braunstein, Chomp, Inc. James Piette, University of Pennsylvania Shane T. Jensen, University of Pennsylvania Recommended Citation: McShane, Blakeley B.; Braunstein, Alexander; Piette, James; and Jensen, Shane T. (2011) "A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics," Journal of Quantitative

toward 0, thus reducing sampling variability. There are many such constraints, hence many shrinkage methods. One of the most important shrinkage methods is the Lasso ( Tibshirani, 2011 ). When the Lasso is applied to a multiple regression problem, small-valued coefficient estimates are reduced to 0 and the remaining coefficient estimates are shrunk by a fixed amount ( Tibshirani, 2013 ). Because of this property, the Lasso is often used for variable selection ( Tibshirani, 1996 ). In Lasso variable selection, the predictors having nonzero coefficient estimates after