Related papers: Post-selection inference for L1-penalized likeliho…
Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…
We consider inference for M-estimators after model selection using a sparsity-inducing penalty. While existing methods for this task require bespoke inference procedures, we propose a simpler approach, which relies on two insights: (i)…
The problem that is solved in this paper is known as index tracking. The method of Lasso is used to reduce the dimensions of S&P500 index which has many applications in both investment and portfolio management algorithms. The novelty of…
In this work a method to regularize Cox frailty models is proposed that accommodates time-varying covariates and time-varying coefficients and is based on the full instead of the partial likelihood. A particular advantage in this framework…
Valid uncertainty quantification after model selection remains challenging in high-dimensional linear regression, especially within the possibilistic inferential model (PIM) framework. We develop possibilistic inferential models for…
The logistic specification has been used extensively in non-Bayesian statistics to model the dependence of discrete outcomes on the values of specified covariates. Because the likelihood function is globally weakly concave estimation by…
Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate through appropriate link functions. On the other…
We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can…
We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…
In this paper, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic…
In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…
We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a…
We extend the theory from Fan and Li (2001) on penalized likelihood-based estimation and model-selection to statistical and econometric models which allow for non-negativity constraints on some or all of the parameters, as well as…
We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…
Sparsity-inducing penalties are useful tools for variable selection and they are also effective for regression settings where the data are functions. We consider the problem of selecting not only variables but also decision boundaries in…
Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the…
We propose a test of the significance of a variable appearing on the Lasso path and use it in a procedure for selecting one of the models of the Lasso path, controlling the Family-Wise Error Rate. Our null hypothesis depends on a set A of…
We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization…