Related papers: Feature-specific inference for penalized regressio…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
Multiple hypothesis testing has been widely applied to problems dealing with high-dimensional data, e.g., selecting significant variables and controlling the selection error rate. The most prevailing measure of error rate used in the…
Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized…
Sparse regularized regression methods are now widely used in genome-wide association studies (GWAS) to address the multiple testing burden that limits discovery of potentially important predictors. Linear mixed models (LMMs) have become an…
High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…
In traditional logistic regression models, the link function is often assumed to be linear and continuous in predictors. Here, we consider a threshold model that all continuous features are discretized into ordinal levels, which further…
Many penalized maximum likelihood estimators correspond to posterior mode estimators under specific prior distributions. Appropriateness of a particular class of penalty functions can therefore be interpreted as the appropriateness of a…
Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average…
We propose a novel approach, Sequential Lasso, for feature selection in linear regression models with ultra-high dimensional feature spaces. We investigate in this article the asymptotic properties of Sequential Lasso and establish its…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of time varying regressors to be larger than the sample size.…
Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…
Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood…
There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on…
In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…
High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…
In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by…
All models may be wrong -- but that is not necessarily a problem for inference. Consider the standard $t$-test for the significance of a variable $X$ for predicting response $Y$ whilst controlling for $p$ other covariates $Z$ in a random…
In the context of high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where the penalty…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…