The current study examined Intolerance of Uncertainty (IU)-the tendency to react negatively to situations that are uncertain-in psychological problems among adolescents. Using data from 191 adolescents, aged 14 to 18, we examined (a) the dimensionality of IU as tapped by the Intolerance of Uncertainty Scale short-form (IUS-12), (b) the relationship of IU with worry, social anxiety, and depression, (c) the specificity of IU to these variables, and (d) the role of IU as a mediator of the linkages between negative affectivity (NA) and worry, social anxiety, and depression. Results showed that the IUS-12 encompassed 2 components of IU, named Prospective Anxiety and Inhibitory Anxiety. Furthermore, IU was specifically related with worry and social anxiety, but not depression, when controlling the shared variance between these variables and NA, age, and gender. Finally, IU and its 2 components were found to mediate the linkages of NA with worry and social anxiety.

Robust selection of variables in a linear regression model is investigated.Many variable selection methods are available, but very few methods are designed to avoid sensitivity to vertical outliers as well as to leverage points. The nonnegative garrote method is a powerful variable selection method, developed originally for linear regression but recently successfully extended to more complex regression models. The method has good performances and its theoretical properties have been established. The aim is to robustify the nonnegative garrote method for linear regression as to make it robust to vertical outliers and leverage points. Several approaches are discussed, and recommendations towards a final good performing robust nonnegative garrote method are given. The proposed method is evaluated via a simulation study that also includes a comparison with existing methods. The method performs very well, and often outperforms existing methods. A real data application illustrates the use of the method in practice.

This paper concerns a robust variable selection method in multiple linear regression: the robust S-nonnegative garrote variable selection method. In this paper the consistency of the method, both in terms of estimation and in terms of variable selection, is established. Moreover, the robustness properties of the method are further investigated by providing a lower bound for the breakdown point, and by deriving the influence function. The provided expressions nicely reveal the impact that the choice of an initial estimator has on the robustness properties of the variable selection method. Illustrative examples of influence functions for the S-nonnegative garrote as well as for the original (non-robust) nonnegative garrote variable selection method are provided.

Selecting among a large set of variables those that influence most a response variable is an important problem in statistics. When the assumed regression model involves a nonparametric component, penalized regression techniques, and in particular P-splines, are among the commonly used methods. The aim of this paper is to provide a brief review of variable selection methods using P-splines. Starting from multiple linear regression models, with least-squares regression, and Ridge regression, we review standard methods that perform variable selection, such as LASSO, nonnegative garrote, the SCAD method, etc. We briefly discuss a general framework of penalization and regularization methods. Going toward more flexible regression models, with some nonparametric component(s), we discuss P-splines estimation. For some examples of flexible regression models, we then review a few variable selection methods using P-splines. A brief discussion on grouped regularization techniques and on a robust variable selection method is given. Furthermore, we mention key ingredients in Bayesian approaches, and end the paper by drawing the attention to several other issues in variable selection with P-splines. Throughout the paper we provide some illustrations. LEAST-SQUARES AND RIDGE REGRESSION In regression analysis the interest is to find out how, on average, a variable of interest Y is influenced by some explanatory variables X 1 , … , X d . In multiple linear regression the relationship between Y and (X 1 , … , X d ) is modeled via T the vector of unknown regression coefficients, and where denotes the error term. The superscript T denotes the transposed of a matrix or a vector.Often measurements on many potential influential factors X 1 , … , X d are available, and selecting among the d variables those that have a significant average influence on the response variable Y, is a major concern.Suppose that an i.i.is available. The ordinary least-squares method consists of solving the optimization problemand results into the least-squares estimatorof . We rewrite the Volume 7, January/February 2015